Research Methods
Running head: SUN COAST REMEDIATION RESEARCH PROJECT 1
SUN COAST REMEDIATION RESEARCH PROJECT 4
Sun Coast Remediation Project
Megan Garrett
Columbia Southern University
Table of Contents Executive Summary 4 Introduction 5 Statement of the Problems 5 Particulate Matter (PM) 5 Safety Training Effectiveness 6 Sound-Level Exposure 6 New Employee Training 6 Lead Exposure 7 Return on Investment 7 Literature Review 7 Research Objectives 10 Research Questions and Hypotheses 11 Research Methodology, Design, and Methods 12 Research Methodology 13 Research Design 13 Research Methods 13 Data Collection Methods 14 Sampling Design 14 Data Analysis Procedures 15 Data Analysis: Descriptive Statistics and Assumption Testing 16 Correlation: Descriptive Statistics and Assumption Testing 16 Simple Regression: Descriptive Statistics and Assumption Testing 19 Multiple Regression: Descriptive Statistics and Assumption Testing 22 Independent Samples t Test: Descriptive Statistics and Assumption Testing 26 Dependent Samples (Paired-Samples) t Test: Descriptive Statistics and Assumption Testing 29 ANOVA: Descriptive Statistics and Assumption Testing 31 Data Analysis: Hypothesis Testing 35 Correlation: Hypothesis Testing 36 Simple Regression: Hypothesis Testing 37 Multiple Regression: Hypothesis Testing 39 Independent Sample t test 42 Dependent Sample t Test 43 ANOVA 44 Findings 46 Recommendations 48 References 49
Executive Summary
Sun Coast Remediation project depend on the research method to make decision on six areas of the concern. Quantities research method is applied where correlation analysis, simple regression analysis, multiple regression analysis, independent t test, paired t test and Anova analysis are used to determine the decision that will be taken with each test statistics representing specific area of the concern. First area is to determine how particulate matter affects health of the employees. From the analysis, there is strong negative association between particulate matter and annual sick days of the employees. This means that microns from the job site has nothing to do about the health of the employees and therefore cannot be related to annual sick days of employees. Second issues is to establish how safety training expenditure is related to the lost time hours. It is found that if the training expenditure increases, lost time hours tends to decrease hence it is necessary for the management to consider investing in training. Third issue was to determine effects of the primary factors to the noisy levels. From the analysis, it has been established that primary factors contribute to high levels of the noise levels above 120 decibels which create need for the management to secure advanced earmuffs for its employees. Fourth area of the concern was to determine if the revised training program is more effective than prior training program. From analysis it has been established that revised training program is more effective hence need of this program to be adopted by the Sun Coast leadership. Fifth area of the analysis was to determine effect of the lead exposure on the blood level. From analysis, lead exposure does not affect blood level. Lastly, it was of the concern to examine if ROI differs across four lines of the service air monitoring, water reclamation, soil remediation and training. From the analysis, it has been established ROI varies across four lines of the services which creates need for the management to determine most profitable and least profitable line.
Introduction
Senior leadership at Sun Coast has identified several areas for concern that they believe could be solved using business research methods. The previous director was tasked with conducting research to help provide information to make decisions about these issues. Although data were collected, the project was never completed. Senior leadership is interested in seeing the project through to fruition. The following is the completion of that project and includes the statement of the problems, literature review, research objectives, research questions and hypotheses, research methodology, design, and methods, data analysis, findings, and recommendations.
Statement of the Problems
Six business problems were identified:
Particulate Matter (PM)
There is a concern that job-site particle pollution is adversely impacting employee health. Although respirators are required in certain environments, PM varies in size depending on the project and job site. PM that is between 10 and 2.5 microns can float in the air for minutes to hours (e.g., asbestos, mold spores, pollen, cement dust, fly ash), while PM that is less than 2.5 microns can float in the air for hours to weeks (e.g. bacteria, viruses, oil smoke, smog, soot). Due to the smaller size of PM that is less than 2.5 microns, it is potentially more harmful than PM that is between 10 and 2.5 since the conditions are more suitable for inhalation. PM that is less than 2.5 is also able to be inhaled into the deeper regions of the lungs, potentially causing more deleterious health effects. It would be helpful to understand if there is a relationship between PM size and employee health. PM air quality data have been collected from 103 job sites, which is recorded in microns. Data are also available for average annual sick days per employee per job-site.
Safety Training Effectiveness
Health and safety training is conducted for each new contract that is awarded to Sun Coast. Data for training expenditures and lost-time hours were collected from 223 contracts. It would be valuable to know if training has been successful in reducing lost-time hours and, if so, how to predict lost-time hours from training expenditures.
Sound-Level Exposure
Sun Coast’s contracts generally involve work in noisy environments due to a variety of heavy equipment being used for both remediation and the clients’ ongoing operations on the job sites. Standard ear-plugs are adequate to protect employee hearing if the decibel levels are less than 120 decibels (dB). For environments with noise levels exceeding 120 dB, more advanced and expensive hearing protection is required, such as earmuffs. Historical data have been collected from 1,503 contracts for several variables that are believed to contribute to excessive dB levels. It would be important if these data could be used to predict the dB levels of work environments before placing employees on-site for future contracts. This would help the safety department plan for procurement of appropriate ear protection for employees.
New Employee Training
All new Sun Coast employees participate in general health and safety training. The training program was revamped and implemented six months ago. Upon completion of the training programs, the employees are tested on their knowledge. Test data are available for two groups: Group A employees who participated in the prior training program and Group B employees who participated in the revised training program. It is necessary to know if the revised training program is more effective than the prior training program.
Lead Exposure
Employees working on job sites to remediate lead must be monitored. Lead levels in blood are measured as micrograms of lead per deciliter of blood (μg/dL). A baseline blood test is taken pre-exposure and postexposure at the conclusion of the remediation. Data are available for 49 employees who recently concluded a 2-year lead remediation project. It is necessary to determine if blood lead levels have increased.
Return on Investment
Sun Coast offers four lines of service to their customers, including air monitoring, soil remediation, water reclamation, and health and safety training. Sun Coast would like to know if each line of service offers the same return on investment. Return on investment data are available for air monitoring, soil remediation, water reclamation, and health and safety training projects. If return on investment is not the same for all lines of service, it would be helpful to know where differences exist.
Literature Review
When research methods are used to develop solution to a particular problem, statistical analysis of different types may be used where in this case, evaluation is done for correlational analysis, simple regression analysis, multiple regression analysis, independent t-test, paired sample t Test and One Way Anova analysis. For better understanding, we review each of the six test statistics describing their appropriate application as explained by different scholars where sequence of the articles will be used where each article relate to a particular test statistics.
In the first article, author explains how correlational analysis is used. The author is Professor and Associate Dean, Research and Graduate studies in the Faculty of Pharmacy in the University Alberta. The author posit that correlation is used to analyze the strength of the relations between two variables such as weight and blood pressure (Simpson, 2015). Considering the Sun Coast problem, one may analyze the strength of the relationship between the job site and microns. This would help determine if the type of association is positive or negative.
In the second article, authors are experienced and scholars from the Department of Anthropology, University of Delhi. They have explained the origin of the linear regression analysis and the reason why it is used. In the explanation, linear regression analysis is used to describe the relationship between two variables through statistical estimation (Kumari & Yadav, 2018). For example, one may want to know if having high blood pressure is influenced by weight, which may require the use of the simple regression analysis. In this article, the subject matter of the linear regression analysis relates to the subject of the simple regression data in the Sun Coast. Sun Coast may use simple regression or linear regression to find out whether safety training will influence #contract.
In the third article, authors are scholars in different departments’ universities and they take time to explain the concept of the multivariate or multiple regression analysis. In the case analysed in the article, multivariate linear regression was used to analyze how sex, age, bone type, insertion torque, implant diameter, implant length and T1-T2 time interval influenced stability prediction for 11 candidates (Huang et al….,2017). In other words, several factors are used to determine how they affect a particular dependent variable. In practical, we assess how # contract is influenced by frequency, angle degrees, chord length, velocity, displacement and decibel.’
In fourth article, authors are scholars in the department of the Anesthesia and Pain Medicine, Pusan National University School of Medicine. In their study, argue that t-test is used to compare the means of two group and establish if there is difference between two means. ). In this article, researchers extracted two samples with a size of 6 from a population N (150, 52) and found the difference in the means. Independent t-test in this article relates to independent t-test data in Sun Coast which would help to find if there is the difference in means between Groups A prior to training scores and Group B Revised training scores.
In fifth article, authors were determined to explain how paired t-test is used. According the authors, paired t test is used to establish that difference between two paired means is equal to zero. For example, there was an examination of the stability of the personality traits where the personality of the particular individuals was measured and later they exposed to a series of training and their personality was measured after this training. It was found that several personality traits were equivalent at pretest and posttest were given several nonsignificant paired-samples t-tests (Mara & Cribbie, 2012). In this article, the subject matter of the discussion relates to the paired sample t-test which desired to establish whether there were changes in the employees before and after exposure to μg/dL.
Lastly, in the sixth article, author reviews ANOVA analysis which looks differences between variances. When the mean of the samples under comparison are more than two, t paired and independent seizes to be appropriate test statistics and instead ANOVA analysis is used. ANOVA is used to avoid hypothesis testing error which occurs due to significance level inflation (Kim, 2017) This article addresses the solution to the problem in tab six of the Sun Coast which is all about ANOVA One- way data where there is Air, Soil, Water and Training. The firm will use ANOVA One- way to determine if there is a statistical level of the significance in the return of the investment that is caused by Air, Soil, Water and Training. Conclusion is made using F test statistics.
Research Objectives
The leadership of the Sun Coast has identified a number of the issues that it believed could be solved using research methods. Research methods (Qualitative, quantitative and mixed research methods) are powerful tools that if they are utilized effectively they can help the firm in developing solutions to some of the problems that it is experiencing (Creswell, & Creswell, 2018). Data has been collected and six areas aim to be addressed. The job site is believed to contribute to some of the problems that are experienced by the firm. The firm conducts safety training to new contracts and also want to understand noisy levels how it affects employees to develop protective mechanisms because some levels such as 115 decibels are considered dangerous (Creative Safety Supply, 2016). Similarly, it concerned about the effectiveness of training programs and productivity of its service lines which is critical in guiding the firm is knowing the program that it should implement and also service line that needs much attention. Six there are six areas of concerns, six objectives are developed which are;
RO1: Establish how particles from the job site (microns) affect the health of the employees.
RO2: Determine if the safety training expenditure to the new contracts aids in reducing lost time hours.
RO3: Investigate primary factors such as velocity that contribute to excessive noise (decibels) work environment.
RO4: Find out if there Group B Revised training is more effective than Group A prior training.
RO5: Establish if there is any change in the blood level before and after lead exposure.
RO6: Determine if there is the difference in the return on investment in four service lines-air, water, soil and training.
Research Questions and Hypotheses
In reference to the research objectives, research question and hypotheses have been developed which finally will be evaluated from the test statistics so that conclusion can be reached. The following are research questions and hypotheses;
RQ1: Is there relationship between particles from the job site and annual sick day per employee?
H01: There is no statistical relationship between particles from the job site and annual sick day per employee.
HA1: There is a statistically significant relationship between particles from the job site and annual sick day per employee.
RQ2: Is there a causal relationship between safety training expenditure and lost time hours?
H02: There is no causal relationship between safety training expenditure and lost time hours.
HA2: There is a statistical significant causal relationship between safety training expenditure and lost time hours.
RQ3: Is there a difference between primary variables such as velocity and decibel levels of the work environment.
H03: There is no significant statistical difference between primary variables such as velocity and decibel levels of the work environment.
HA3: There is the significant statistical difference between primary variables such as velocity and decibel levels of the work environment.
RQ4: Is Group B revised training more effective than Group A prior training.
H04: Group B revised training is no more effective than Group A prior training.
HA4: Group B revised training is more effective than Group A prior training.
RQ5: Is there a difference in the blood level after and before lead exposure?
H05: There is no significant statistical difference between blood levels before and after lead exposure.
HA5: There is the significant statistical difference between blood levels before and after lead exposure.
RQ6: Is there a difference in return on investment in four service lines air, water, soil and training?
H06: There is no significant difference in return on investment in four service lines air, water, soil and training.
HA6: There is a significant difference in return on investment in four service lines air, water, soil and training.
Research Methodology, Design, and Methods
The leadership of the Sun Coast requires to collect information that will be used to solve the problem that it is experiencing. Effective use of the quantitative method help to develop some of the solutions that solve some of the problems that are experienced by Sun Coast (Creswell, & Creswell, 2018). Research design that is consistent with the methodological process that is chosen. Given the nature of the information that needs to be collected, a research design that needs to be collected may be applied for the case of Sun Coast is non-experimental research design. In addition, research methods for the Sun Coast that will be used in this project will depend on the research design that has been chosen
Research Methodology
The quantitative research methodology will be used in the Sun Coast project. This is because depending on six areas of the interest that are investigated by the Sun Coast numerical data will be critical. Numerical data is needed to determine the association that exists between job sites. Numerical data of the expenditure and work hours used in simple regression provides sufficient reason for the choice of the quantitative research method which is not possible if the qualitative method is used. Lastly, in the research, would be interested to determine the relationship that exists between various variables such effectiveness prior training and revised training which suitable with quantitative research method against qualitative research method (Patten & Newhart, 2017).
Research Design
For the case of the Sun Coast project, research design that is most appropriate is non-experimental. This is because it does not involve laboratory experiments that require controlled and treatment but data is collected on various variables of the interest and interpretation is made based on the observation which is used to inform conclusion that is reached (Patten & Newhart, 2017). Depending on the nature of the research question and hypothesis, a non-experimental research design that may be used for Sun Coast are correlational and causal-comparative methods. The correlational method may be used for question 1 while causal-comparative method will be used for question 2, 3, 4, 5 and 6.
Research Methods
Research methods that are used depend on the research questions that need one need to respond to which also determine how hypotheses are framed. For question and hypothesis 1, correlational research method will be used because it establishes the association that exists between job sites and annual sick days per employee. Causal- comparative research is used for question 2, 3, 4, 5 and 6. This because of the following reasons; for question 2, is used to determine causal relationship that exists expenditure in the safety training and lost hours; question 3, causal relationship that exist between primary variables and decibels; question 4, causal-comparison of effectiveness of the training method used; question 5, causal relationship for change in the blood level exposed to lead and lastly, causal –comparison of the ROI for the four service lines.
Data Collection Methods
For question one, record analysis used to collect data on the microns and also annual sick day per employee. For question 2, information on the training expenditure and lost hours may be collected using a questionnaire sent to contractors to fill. For question 3, data on the primary variables that influence noise levels were collected possibly using record analysis. Question 4, scores to the prior training and revised training were mostly collected using record analysis. The question, information on the changes to blood level before and after lead exposure were collected mostly through observation while data for question 6 was mostly collected through survey.
Sampling Design
In question 1, 3, 4 and 5 random sampling design were mostly used for the data that was collected. This because data that was collected was numerical and the chance of occurring of any particular observation was equal. However, for question 2 and 3, convenience sampling would be used for the data for the collected data because it involves quite a number of the observation and researcher would find it necessary use the data that seems convenient to him or her.
Data Analysis Procedures
For the RQ1 hypotheses, correlation is preferred because it helps to determine the association that exists between microns in the job site and annual sick days per employee. Information provided using correlation analysis is the degree of the association and whether the association is positive or negative (Simpson, 2015).
For the RQ2 hypotheses, simple regression analysis is preferred because it determines if there is a causal relationship that exists between expenditure training and lost hours (Kumari & Yadav, 2018). Point of interest would be whether the increase in expenditure training reduces lost hours.
For the RQ3 hypotheses, multiple regression analysis is preferred because more than primary variables (independent variables) are used to assess how they influence the dependent variable (Huang et al….,2017). In particular, point of interest would be how frequency, angle in degrees, chord length, displacement and velocity influence decibels.
In the RQ4 hypotheses, the independent t-test is preferred because it helps in determining whether two training methods are different. Mean of prior training is compared against revised training and if the difference between two is zero, then the conclusion will be made that there is no difference between the two samples (Kim, 2015).
In the RQ5 hypotheses, paired t-test us preferred because it wants to determine that there is a difference that exists between two independent samples (Mara & Cribbie, 2012). In particular, if there is a difference in blood level before and after exposure to the lead, then the conclusion will then be made that there is a statistical difference between the two samples.
Lastly, in the RQ6 hypotheses, ANOVA one way data is preferred because the comparison is made against more than 2 samples (Kim, 2017). In this particular case, we would like to determine if ROI is different soil, water, air and training. Therefore, the only statistical procedure that is able to provide information that is needed in this question is only ANOVA one way data analysis.
Data Analysis: Descriptive Statistics and Assumption Testing
In the Sun Coast remediation project, descriptive tools such as frequency distribution table, histogram, descriptive summary table and measure of the central tendency are used to describe the data. In the Sun remediation, it has been established earlier that quantitative research method has been preferred because the remediation data is numerical and also it is believed that it is the research method that will deliver solution that is desired by the senior leadership (Creswell & Creswell, 2018). Using the descriptive statistic, we are able to determine if the data meets assumption for the parametric testing. First, distribution is assumed to be normally distributed which is the main assumption of the parametric testing (Hopkins, Dettori & Chapman, 2018). It is established with use of histogram which is symmetrical or kurtosis that is equal to zero. Homogeneity of the variances is another assumption that is used which posit that when given groups of the data, variance of the samples are the same (Kim & Park, 2019). Third, for the parametric testing to be used is assumed that the variables have linear relationship which can be established using scatter diagrams or correlation, linear regression and multiple regression. Lastly, it independence of the variables is another assumption that is used to qualify use of the parametric testing (Nimon, 2012). Considering the descriptive statistics in each tab in the Excel, we will be able to determine we will be able to determine if the Sun Coast remediation data meets parametric assumptions or not.
Correlation: Descriptive Statistics and Assumption Testing
Frequency distribution table.
|
Bin |
Frequency |
|
2 |
1 |
|
3 |
1 |
|
4 |
5 |
|
5 |
13 |
|
6 |
18 |
|
7 |
24 |
|
8 |
18 |
|
9 |
12 |
|
10 |
7 |
|
11 |
2 |
|
More |
2 |
Histogram
Descriptive statistics table.
|
|
|
|
Descriptive summary |
|
|
|
|
|
Mean |
7.126214 |
|
Standard Error |
0.186484 |
|
Median |
7 |
|
Mode |
7 |
|
Standard Deviation |
1.892605 |
|
Sample Variance |
3.581953 |
|
Kurtosis |
0.124923 |
|
Skewness |
0.14225 |
|
Range |
10 |
|
Minimum |
2 |
|
Maximum |
12 |
|
Sum |
734 |
|
Count |
103 |
Measurement scale.
The measurement scale for the dependent variable is ratio scale. This is because ratio scale is continuous and start from zero. Data of the annual sick days per employee may be put in the continuous scale and this is the reason why is able to come up with frequency distribution table.
Measure of central tendency.
Mean of the annual sick day of the employees are 7.126 while median and mode annual sick days of the employees are 7. From the descriptive summary, mode, median and mean are almost similar which is an important indicator of the normality of the distribution.
Evaluation.
From the descriptive statistics, mean=mode=median. This is an important element for the normal distribution. Second, histogram is symmetrical which indicate that dependent variable is normally distributed. Based on these two factors, conclusion can be reached that this data set meets criteria for the parametric testing because it meets the main assumption of the parametric testing that is, distribution is normally distributed (Hopkins, Dettori & Chapman, 2018).
Simple Regression: Descriptive Statistics and Assumption Testing
Frequency distribution table
|
Bin |
Frequency |
|
10 |
1 |
|
35 |
1 |
|
60 |
9 |
|
85 |
9 |
|
110 |
17 |
|
135 |
18 |
|
160 |
24 |
|
185 |
27 |
|
210 |
37 |
|
235 |
24 |
|
260 |
21 |
|
285 |
15 |
|
310 |
12 |
|
335 |
4 |
|
More |
4 |
Histogram.
Descriptive statistics table.
|
|
Descriptive Statistics |
|
|
|
|
|
|
|
Mean |
188.0045 |
|
|
Standard Error |
4.803089 |
|
|
Median |
190 |
|
|
Mode |
190 |
|
|
Standard Deviation |
71.72542 |
|
|
Sample Variance |
5144.536 |
|
|
Kurtosis |
-0.50122 |
|
|
Skewness |
-0.08198 |
|
|
Range |
350 |
|
|
Minimum |
10 |
|
|
Maximum |
360 |
|
|
Sum |
41925 |
|
|
Count |
223 |
Measurement scale.
Measurement scale that is used in this dependent variable is interval scale. This is because time has equal interval between each variables. The dependent variable which is the lost time in hours, difference between hours are equal.
Measure of central tendency.
There are three main variables that are mostly used in measuring central of the tendency. First, it is the mean. The average or the mean lost hours are 188.0045. Second, it is the mode which is the most common variable. The mode for the lost hours is 190. The last component is the median which id the middle value when data is arranged from ascending to descending order or vice versa. The median lost hours are 190. Considering the three main elements of the measure of the central tendency, conclusion can be made that mode=mean=median and therefore, lost time hours are normally distributed.
Evaluation.
From the descriptive statistics, mode=mean=median which means that lost time hours are normally distributed. Second, histogram provides clearer picture that demonstrate that data from this dependent variable (lost time hours) is normally distributed. Since measure of central tendency and histogram confirm that data is normally distributed, then conclusion can be reached that simple regression data set meets assumptions of parametric testing.
Multiple Regression: Descriptive Statistics and Assumption Testing
Frequency distribution table.
|
Bin |
Frequency |
|
103.38 |
1 |
|
104.3697 |
2 |
|
105.3593 |
1 |
|
106.349 |
3 |
|
107.3386 |
6 |
|
108.3283 |
6 |
|
109.3179 |
9 |
|
110.3076 |
12 |
|
111.2973 |
18 |
|
112.2869 |
17 |
|
113.2766 |
26 |
|
114.2662 |
22 |
|
115.2559 |
27 |
|
116.2456 |
47 |
|
117.2352 |
36 |
|
118.2249 |
44 |
|
119.2145 |
47 |
|
120.2042 |
53 |
|
121.1938 |
61 |
|
122.1835 |
60 |
|
123.1732 |
62 |
|
124.1628 |
74 |
|
125.1525 |
70 |
|
126.1421 |
81 |
|
127.1318 |
93 |
|
128.1214 |
73 |
|
129.1111 |
105 |
|
130.1008 |
80 |
|
131.0904 |
88 |
|
132.0801 |
67 |
|
133.0697 |
50 |
|
134.0594 |
56 |
|
135.0491 |
35 |
|
136.0387 |
30 |
|
137.0284 |
19 |
|
138.018 |
7 |
|
139.0077 |
8 |
|
139.9973 |
5 |
|
More |
2 |
Histogram.
Descriptive statistics table.
|
|
|
|
|
|
Descriptive statistics |
|
|
|
|
|
|
|
Mean |
124.8359 |
|
|
Standard Error |
0.177945 |
|
|
Median |
125.721 |
|
|
Mode |
127.315 |
|
|
Standard Deviation |
6.898657 |
|
|
Sample Variance |
47.59146 |
|
|
Kurtosis |
-0.31419 |
|
|
Skewness |
-0.41895 |
|
|
Range |
37.607 |
|
|
Minimum |
103.38 |
|
|
Maximum |
140.987 |
|
|
Sum |
187628.4 |
|
|
Count |
1503 |
Measurement scale.
Interval measurement scale is most preferable for decibel dependent variable. This is because dependent variable is measured on the continuous scale.
Measure of central tendency.
Mean of the data of the dependent variable is 124.83, mode is 127.32 while the median is 125.72. By taking closer look at mean, mode and median, the difference between them is insignificant hence they are almost the same. Therefore, we use of the measure of the central tendency, argument can be made that data is normally is distributed.
Evaluation
Measures of the central tendency confirm that the dependent variable data is normally distributed. Second, histogram plotted is symmetrical which shows that data under consideration is normally distributed. In general, the data meets parametric test and can be used because it is normally distributed.
Independent Samples t Test: Descriptive Statistics and Assumption Testing
Frequency distribution table.
Group A Prior Training Group B Revised Training
|
Bin |
Frequency |
|
50 |
4 |
|
55.85714 |
5 |
|
61.71429 |
7 |
|
67.57143 |
8 |
|
73.42857 |
14 |
|
79.28571 |
10 |
|
85.14286 |
8 |
|
More |
6 |
|
Bin |
Frequency |
|
75 |
2 |
|
78.14286 |
5 |
|
81.28571 |
10 |
|
84.42857 |
12 |
|
87.57143 |
14 |
|
90.71429 |
11 |
|
93.85714 |
5 |
|
More |
3 |
Histogram.
Group A Group B
Descriptive statistics table.
|
Descriptive statistics Group A |
|
|
Descriptive Statistics Group B |
|
|
|
|
|
|
|
|
|
|
Mean |
|
|
Mean |
84.77419 |
|
|
Standard Error |
|
|
Standard Error |
0.659479 |
|
|
Median |
|
|
Median |
85 |
|
|
Mode |
|
|
Mode |
85 |
|
|
Standard Deviation |
|
|
Standard Deviation |
5.192742 |
|
|
Sample Variance |
|
|
Sample Variance |
26.96457 |
|
|
Kurtosis |
|
|
Kurtosis |
-0.35254 |
|
|
Skewness |
|
|
Skewness |
0.144085 |
|
|
Range |
|
|
Range |
22 |
|
|
Minimum |
|
|
Minimum |
75 |
|
|
Maximum |
|
|
Maximum |
97 |
|
|
Sum |
|
|
Sum |
5256 |
|
|
Count |
|
|
Count |
62 |
|
Measurement scale.
Ordinal measurement scale is preferable for both groups is ordinal scale. This is because it scores that are attained by the Group A prior to training and also Group B Revised training can be ranked and difference be calculated to ascertain that there is no difference in the mean of the two samples.
Measure of central tendency.
Prior training scores for the Group A mean is 69.79, mode is 80 and median 70 while Group B revised training score are 84.77, mode and median is 85.From this information, measures of the tendency for Group A shows significant variation hence conclusion cannot be made that data is normally distributed. However, for Group B, measures of the central tendency are almost the same and conclusion can be made that distribution is normally distributed.
Evaluation.
Descriptive statistics for the Group A shows mean, mode and median are not equal hence violate normality of the distribution. However, histogram demonstrates that otherwise because it shows that distribution is symmetrical hence showing that the distribution is normally distributed. On the other hand, measures of the central tendency are almost equal and also histogram is symmetrical which strongly shows that data is normally is distributed. Further, there is independence of the two data samples. Considering these two reasons which are independence of the samples and normality of the distribution, the data variables qualify for parametric testing assumption (Nimon, 2012; Hopkins, Dettori & Chapman, 2018).
Dependent Samples (Paired-Samples) t Test: Descriptive Statistics and Assumption Testing
Frequency distribution table.
Pre-Exposure μg/dL Post-Exposure μg/dL
|
Bin |
Frequency |
|
Bin |
Frequency |
|
6 |
1 |
|
6 |
1 |
|
13.14286 |
3 |
|
13.14286 |
3 |
|
20.28571 |
5 |
|
20.28571 |
5 |
|
27.42857 |
6 |
|
27.42857 |
6 |
|
34.57143 |
8 |
|
34.57143 |
8 |
|
41.71429 |
13 |
|
41.71429 |
11 |
|
48.85714 |
9 |
|
48.85714 |
11 |
|
More |
4 |
|
More |
4 |
Histogram.
Pre-Exposure μg/dL Post-Exposure μg/dL
Descriptive statistics table.
|
Descriptive statistics Pre-Exposure μg/dL |
|
|
|
|
|
Mean |
32.85714 |
|
Standard Error |
1.752307 |
|
Median |
35 |
|
Mode |
36 |
|
Standard Deviation |
12.26615 |
|
Sample Variance |
150.4583 |
|
Kurtosis |
-0.57604 |
|
Skewness |
-0.42511 |
|
Range |
50 |
|
Minimum |
6 |
|
Maximum |
56 |
|
Sum |
1610 |
|
Count |
49 |
|
Descriptive Statistics Post-Exposure μg/dL |
|
|
|
|
|
Mean |
33.28571 |
|
Standard Error |
1.781423 |
|
Median |
36 |
|
Mode |
38 |
|
Standard Deviation |
12.46996 |
|
Sample Variance |
155.5 |
|
Kurtosis |
-0.65421 |
|
Skewness |
-0.48363 |
|
Range |
50 |
|
Minimum |
6 |
|
Maximum |
56 |
|
Sum |
1631 |
|
Count |
49 |
Measurement scale.
Ratio scale of the measurement is preferred in the paired-test because dependent variable must be continuous.
Measure of central tendency.
For the paired t-test two components are very significant which are mean and median. Mean of the blood level before lead exposure was 32.86 while its median was 35. On the other hand, mean of the blood level after lead exposure was 33.29 while its median was 36. Therefore, comparing the difference modes of the corresponding samples as well that of the means, it is insignificant hence no difference of the blood level after lead exposure.
Evaluation.
Mode sample 1 = mode in sample 2 and mean sample 1=mean sample in 2 hence difference between two paired samples is equal to zero. Further, histogram diagram for the two samples are almost symmetrical which shows that data is normally distributed. Observations are independent of the each other and the dependent variables are continuous. Variances of the two samples are approximately equal, with sample variance for pre-exposure being 150 while for the Post-exposure is 155. Based on this information, paired t-test meets assumption for the parametric testing.
ANOVA: Descriptive Statistics and Assumption Testing
Frequency distribution table.
Air/A Soil/B
|
|
|
|
Bin |
Frequency |
|
Bin |
Frequency |
|
6 |
1 |
|
3 |
1 |
|
7.75 |
2 |
|
5.75 |
3 |
|
9.5 |
10 |
|
8.5 |
4 |
|
11.25 |
5 |
|
11.25 |
8 |
|
More |
2 |
|
More |
4 |
|
||
|
|
|
|
Water /C Training/D
|
Bin |
Frequency |
|
Bin |
Frequency |
|
3 |
1 |
|
3 |
1 |
|
5.25 |
5 |
|
4.25 |
3 |
|
7.5 |
8 |
|
5.5 |
7 |
|
9.75 |
2 |
|
6.75 |
6 |
|
More |
4 |
|
More |
3 |
Histogram.
Air/A B=Soil
C=Water D=Training
Descriptive statistics table.
A=Air B=Soil
|
Descriptive statistics Air |
|
|
|
|
|
Mean |
8.9 |
|
Standard Error |
0.684028 |
|
Median |
9 |
|
Mode |
11 |
|
Standard Deviation |
3.059068 |
|
Sample Variance |
9.357895 |
|
Kurtosis |
-0.6283 |
|
Skewness |
-0.36085 |
|
Range |
11 |
|
Minimum |
3 |
|
Maximum |
14 |
|
Sum |
178 |
|
Count |
20 |
|
|
Descriptive Analysis soil |
|
|
|
|
|
|
|
Mean |
9.1 |
|
|
Standard Error |
0.390007 |
|
|
Median |
9 |
|
|
Mode |
8 |
|
|
Standard Deviation |
1.744163 |
|
|
Sample Variance |
3.042105 |
|
|
Kurtosis |
0.11923 |
|
|
Skewness |
0.492002 |
|
|
Range |
7 |
|
|
Minimum |
6 |
|
|
Maximum |
13 |
|
|
Sum |
182 |
|
|
Count |
20 |
C=Water D=Training
|
Descriptive Analysis |
|
|
|
|
|
Mean |
7 |
|
Standard Error |
0.575829 |
|
Median |
6 |
|
Mode |
6 |
|
Standard Deviation |
2.575185 |
|
Sample Variance |
6.631579 |
|
Kurtosis |
-0.23752 |
|
Skewness |
0.760206 |
|
Range |
9 |
|
Minimum |
3 |
|
Maximum |
12 |
|
Sum |
140 |
|
Count |
20 |
|
|
Descriptive Analysis |
|
|
|
|
|
|
|
Mean |
5.4 |
|
|
Standard Error |
0.265568 |
|
|
Median |
5 |
|
|
Mode |
5 |
|
|
Standard Deviation |
1.187656 |
|
|
Sample Variance |
1.410526 |
|
|
Kurtosis |
0.253747 |
|
|
Skewness |
0.159183 |
|
|
Range |
5 |
|
|
Minimum |
3 |
|
|
Maximum |
8 |
|
|
Sum |
108 |
|
|
Count |
20 |
Measurement scale.
Measurement scale is ratio because dependent variable must be continuous. In this particular assignment, it is expected that data regarding different service lines (air, water, soil and training) is continuous which require ratio scale to be used.
Measure of central tendency.
Mean of the ROI from AIR was 8.9., median 9 and mode 11; mean of ROI from soil was 9.1, median 9 and mode was 8; mean of the ROI from water was 7 while mode and median was 6 and lastly, mean of the ROI from training was 5.4 while median and mode was 5.
Evaluation.
Histograms from four variables are all symmetrical which indicates that data is approximately distributed normally. The four samples are independent of each other. However, variances of the samples are not approximately equal but this does not disqualify use of the ANOVA because assumption of the normality has been upheld. Therefore, parametric testing will be used because all samples used are of the equal size, independent of the each and they are normally distributed as shown by histograms.
Data Analysis: Hypothesis Testing
Hypothesis testing is based on the assumption of the (statistical) null hypothesis, which states that there is no relationship or difference between treatment effects on the outcome. From hypotheses testing decisions is made whether to accept or reject the null hypothesis (Sacha & Panagiotakos, 2016). Using the Sun Cost Remediation data set will be able to conduct a correlation analysis, simple regression analysis, and multiple regression analysis. For the case of the regression, hypotheses will display and discuss the predictive regression equations
Correlation: Hypothesis Testing
Ho1: There is no statistical relationship between particles from the job site and annual sick day per employee.
Ha1: There is a statistically significant relationship between particles from the job site and annual sick day per employee
|
Correlation |
||
|
|
Microns |
Mean annual sick days per employee |
|
Microns |
1 |
-0.71598
|
|
Mean annual sick days per employee |
-0.71598
|
1 |
|
N |
103 |
103 |
|
P-Value |
0.23 |
|
|
R2 |
0.512633
|
Interpretation
The Pearson correlation coefficient of r = -0.71598. This indicates a moderately strong negative correlation. This equates to an r2 of 0.512633 explaining 51% of the variance between the variables.
Using an alpha of .05, the results indicate a p-value of .23 > .05. Therefore, fail to reject the hypothesis, and the alternative hypothesis rejected. Therefore, there is no statistical relationship between particles from the job site and annual sick day per employee.
Simple Regression: Hypothesis Testing
Ho2: There is no causal relationship between safety training expenditure and lost time hours
Ha2: There is a statistically significant causal relationship between safety training expenditure and lost time hours.
|
SUMMARY OUTPUT |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Regression Statistics |
|
|
|
|
|
|
|
|
|
|
Multiple R |
0.937994 |
|
|
|
|
|
|
|
|
|
R Square |
0.879833 |
|
|
|
|
|
|
|
|
|
Adjusted R Square |
0.879286 |
|
|
|
|
|
|
|
|
|
Standard Error |
160.4165 |
|
|
|
|
|
|
|
|
|
Observations |
222 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
ANOVA |
|
|
|
|
|
|
|
|
|
|
|
df |
SS |
MS |
F |
Significance F |
|
|
|
|
|
Regression |
1 |
41450897 |
41450897 |
1610.779 |
3.4E-103 |
|
|
|
|
|
Residual |
220 |
5661360 |
25733.45 |
|
|
|
|
|
|
|
Total |
221 |
47112257 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Coefficients |
Standard Error |
t Stat |
P-value |
Lower 95% |
Upper 95% |
Lower 95.0% |
Upper 95.0% |
|
|
Intercept |
1743.37 |
30.69459 |
56.79731 |
2E-133 |
1682.877 |
1803.863 |
1682.877 |
1803.863 |
|
|
10 |
-6.11019 |
0.152243 |
-40.1345 |
3.4E-103 |
-6.41023 |
-5.81015 |
-6.41023 |
-5.81015 |
|
|
|
|
|
|
|
|
|
|
|
|
Interpretation
From the summary output, simple regression equation will be, Y (Safety Training Expenditure) =1743.37-6.11019 (lost time hours). This means, for each unit increase in the lost time hours, safety training expenditure decreases by 6.11019.
Multiple R is 0.9379 which means that there is a strong positive multiple correlation between safety training expenditure and lost time hours. Considering R squared, 88% of the variation in the safety training expenditure is explained by the lost time hours. P-value is less than alpha hence reject the null hypothesis and accept the alternative hypothesis. Therefore, there is a statistically significant causal relationship between safety training expenditure and lost time hours. F value is less than 0.05 which means that the model is statistically significant. A P-value of lost time hours is less than 0.05 which means that it is statistically significant.
Multiple Regression: Hypothesis Testing
Ha3: There is no significant statistical difference between primary variables such as velocity and decibel levels of the work environment.
Ha3: There is a significant statistical difference between primary variables such as velocity and decibel levels of the work environment.
|
SUMMARY OUTPUT |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Regression Statistics |
|
|
|
|
|
|
|
|
|
|
Multiple R |
0.601842 |
|
|
|
|
|
|
|
|
|
R Square |
0.362214 |
|
|
|
|
|
|
|
|
|
Adjusted R Square |
0.360083 |
|
|
|
|
|
|
|
|
|
Standard Error |
5.518566 |
|
|
|
|
|
|
|
|
|
Observations |
1503 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
ANOVA |
|
|
|
|
|
|
|
|
|
|
|
Df |
SS |
MS |
F |
Significance F |
|
|
|
|
|
Regression |
5 |
25891.89 |
5178.378 |
170.0361 |
2.1E-143 |
|
|
|
|
|
Residual |
1497 |
45590.49 |
30.45457 |
|
|
|
|
|
|
|
Total |
1502 |
71482.38 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Coefficients |
Standard Error |
t Stat |
P-value |
Lower 95% |
Upper 95% |
Lower 95.0% |
Upper 95.0% |
|
|
Intercept |
126.8225 |
0.62382 |
203.2997 |
0 |
125.5988 |
128.0461 |
125.5988 |
128.0461 |
|
|
Frequency (Hz) |
-0.00112 |
4.76E-05 |
-23.4885 |
4.1E-104 |
-0.00121 |
-0.00102 |
-0.00121 |
-0.00102 |
|
|
Angle in Degrees |
0.047342 |
0.037308 |
1.268957 |
0.204654 |
-0.02584 |
0.120524 |
-0.02584 |
0.120524 |
|
|
Chord Length |
-5.49532 |
2.927962 |
-1.87684 |
0.060734 |
-11.2387 |
0.248026 |
-11.2387 |
0.248026 |
|
|
Velocity (Meters per Second) |
0.08324 |
0.0093 |
8.950317 |
1.02E-18 |
0.064997 |
0.101482 |
0.064997 |
0.101482 |
|
|
Displacement |
-240.506 |
16.51903 |
-14.5593 |
5.21E-45 |
-272.909 |
-208.103 |
-272.909 |
-208.103 |
|
Interpretation
From the coefficients, multiple regression equation is as follows; Y (Decibels) =126.82-0.00112Frequencey+0.0473 Angle in Degrees-5.49532 Chord length+0.08324velocity-240.506 displacement. From the equation, holding all factors constant, each unit increase in frequency will lead to decibels increase by 0.00112, a unit increase in angels in degrees will lead to 0.0473 increase in decibels, each unit increase in Chord length will lead to decibels decrease by 5.49532, a unit increase in velocity will lead to decibels increase by 0.08324 and a unit increase in displacement will lead to decibels decrease by 240.506.
Frequency displacement and velocity have their p-values less than 0.05 hence they are statistically significant while chord length and angels in degrees have their p-values greater than 0.05 hence they are insignificant.
Significance F is less than alpha (0.05) hence the model is statistically significant hence we reject the null hypothesis and accept the alternative hypothesis that is- there is the significant statistical difference between primary variables such as velocity and decibel levels of the work environment. There is a positive multiple correlation between the dependent variable and predictor variables. Lastly, predictor variables account for 36% variation in the dependent variables.
Independent Sample t test
Ho4: Group B revised training is no more effective than Group A prior training.
Ha4: Group B revised training is more effective than Group A prior training.
|
t-Test: Two-Sample Assuming Unequal Variances |
|
|
|
|
|
|
|
|
|
|
Group A Prior Training Scores |
Group B Revised Training Scores |
|
|
Mean |
69.79032 |
84.77419 |
|
|
Variance |
122.0045 |
26.96457 |
|
|
Observations |
62 |
62 |
|
|
Hypothesized Mean Difference |
0 |
|
|
|
Df |
87 |
|
|
|
t Stat |
-9.66656 |
|
|
|
P(T<=t) one-tail |
9.7E-16 |
|
|
|
t Critical one-tail |
1.662557 |
|
|
|
P(T<=t) two-tail |
1.94E-15 |
|
|
|
t Critical two-tail |
1.987608 |
|
|
Interpretation of t Test.
From the data output results above, P-value< α therefore reject null hypothesis. In conclusion, there is significant statistical difference between Revised Group B training and Group A prior Training. In this regard, alternative hypothesis holds that Revised Group B training is more effective than Group A prior training.
Dependent Sample t Test
Ho5: There is no significant statistical difference between blood levels before and after lead exposure.
Ha5: There is the significant statistical difference between blood levels before and after lead exposure.
|
t-Test: Paired Two Sample for Means |
|
|
|
|
|
|
|
|
|
|
Pre-Exposure μg/dL |
Post-Exposure μg/dL |
|
|
Mean |
32.85714 |
33.28571 |
|
|
Variance |
150.4583 |
155.5 |
|
|
Observations |
49 |
49 |
|
|
Pearson Correlation |
0.992236 |
|
|
|
Hypothesized Mean Difference |
0 |
|
|
|
Df |
48 |
|
|
|
t Stat |
-1.9298 |
|
|
|
P(T<=t) one-tail |
0.029776 |
|
|
|
t Critical one-tail |
1.677224 |
|
|
|
P(T<=t) two-tail |
0.059553 |
|
|
|
t Critical two-tail |
2.010635 |
|
|
|
|
|
|
|
Interpretation of t Test Results.
From the summary output results above P (T<=t) two-tail which is 0.059553 > α which is 0.05. This means since p –value is greater than alpha, we accept the null hypothesis. In general, it basically mean that there is there is no significant statistical difference between blood levels before and after lead exposure. This is also affirmed by test statistics because t Critical two-tail which is 2.010635 is greater than t Stat which is -1.9298.
ANOVA
H06: There is no significant difference in return on investment in four service lines air, water, soil and training
Ha6: There is a significant difference in return on investment in four service lines air, water, soil and training.
|
|
Anova: Single Factor |
|
|
|
|
|
||
|
|
|
|
|
|
|
|
|
|
|
|
SUMMARY |
|
|
|
|
|
|
|
|
|
Groups |
Count |
Sum |
Average |
Variance |
|
|
|
|
|
A = Air |
20 |
178 |
8.9 |
9.357895 |
|
|
|
|
|
B = Soil |
20 |
182 |
9.1 |
3.042105 |
|
|
|
|
|
C = Water |
20 |
140 |
7 |
6.631579 |
|
|
|
|
|
D = Training |
20 |
108 |
5.4 |
1.410526 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
ANOVA |
|
|
|
|
|
|
|
|
|
Source of Variation |
SS |
df |
MS |
F |
P-value |
F crit |
|
|
|
Between Groups |
182.8 |
3 |
60.93333 |
11.9231 |
1.76E-06 |
2.724944 |
|
|
|
Within Groups |
388.4 |
76 |
5.110526 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Total |
571.2 |
79 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Interpretation
From the output results summary table, P-value is 1.76E-06 which is less than alpha (0.05). This means we reject the null hypothesis and conclude that there is a significant difference in return on investment in four service lines air, water, soil and training.
Findings
Following the statement of the problem addressed in this research project, quantitative research method has been used and results have been analyzed for the Sun Coast to confirm if research objectives are met. Aim of RO1 is to establish how particles from the job site (microns) affect the health of the employees. From the results of the analysis, the Pearson correlation coefficient of r = -0.71598. This indicates a moderately strong negative correlation. Using an alpha of .05, the results indicate a p-value of .23 > .05. Therefore, fail to reject null hypothesis, and the alternative hypothesis rejected. Therefore, there is no statistical relationship between particles from the job site and annual sick day per employee. This suggest that microns from job site does not affects health of the employees but even though it good to ensure reduce particulate matter.
Aim of RO2 is to determine if the safety training expenditure to the new contracts aids in reducing lost time hours. Using regression equation; Y (Safety Training Expenditure) =1743.37-6.11019 (lost time hours). This means, for each unit increase in the lost time hours, safety training expenditure decreases by 6.11019. This basically mean that when safety training expenditure is increased for new contract, lost time hours will be reduced. Further, P-value is less than alpha which signifies that there is a statistically significant causal relationship between safety training expenditure and lost time hours.
Aim of RO3 is to investigate primary factors such as velocity that contribute to excessive noise (decibels) work environment. Multiple regression analysis: Y (Decibels) =126.82-0.00112Frequencey+0.0473 Angle in Degrees-5.49532 Chord length+0.08324velocity-240.506 displacement. From the equation, holding all factors constant, each unit increase in frequency will lead to decibels increase by 0.00112, a unit increase in angels in degrees will lead to 0.0473 increase in decibels, each unit increase in Chord length will lead to decibels decrease by 5.49532, a unit increase in velocity will lead to decibels increase by 0.08324 and a unit increase in displacement will lead to decibels decrease by 240.506. From the results, velocity and angles in degrees contribute to excessive decibel. Results of the analysis suggests that, primary factors contribute to high levels of the decibels hence employees need advanced earmuffs for ear protection.
Aim of RO4 is to find out if there Group B Revised training is more effective than Group A prior training. From test results, P-value< α therefore reject null hypothesis. This implies that revised Group B training is more effective than Group A prior training.
Aim of RO5 is to establish if there is any change in the blood level before and after lead exposure. Results of the study shows that above P (T<=t) two-tail which is 0.059553 > α 0.05. This means that we accept null hypothesis hence there is no significant statistical difference between blood levels before and after lead exposure.
Aim of RO6 is to determine if there is the difference in the return on investment in four service lines-air, water, soil and training. The results shows that P-value is 1.76E-06 which is less than alpha (0.05). This means we reject the null hypothesis and conclude that there is a significant difference in return on investment in four service lines air, water, soil and training.
Recommendations
Based on the results from test statistic and findings presented in the preceding section, the following are the recommendations to the Sun Coast leadership; first, management should investigate what is cause of the sickness among the employees because their annual sick days is not associate with microns on the job site; second, leadership should increases safety training to the new contracts; third leadership should provide advanced earmuffs to employees to protect their ears from noise damage; fourth, Sun Coast should enact revised training program and lastly, Sun Coast should determine service line to invest in because return on investment differs across the four service lines.
References
Creative Safety Supply. (2016).OSHA Hearing Protection Requirements. Retrieved from https://www.creativesafetysupply.com/articles/oshahearingprotection-requirements/
Creswell, J. W., & Creswell, J. D. (2018). Research design: Qualitative, quantitative, and mixed methods approaches (5th ed.). Thousand Oaks, CA: Sage
Hopkins, S., Dettori, J. R., & Chapman, J. R. (2018). Parametric and Nonparametric Tests in Spine Research: Why Do They Matter?. Global spine journal, 8(6), 652-654.
Huang, H., Xu, Z., Shao, X., Wismeijer, D., Sun, P., Wang, J., & Wu, G. (2017). Multivariate linear regression analysis to identify general factors for quantitative predictions of implant stability quotient values. PloS one, 12(10), e0187010.
Kim T. K. (2015). T test as a parametric statistic. Korean journal of anesthesiology, 68(6), 540–546. doi:10.4097/kjae.2015.68.6.540
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Histogram
Frequency 103.38 104.3696579 105.3593158 106.3489737 107.3386316 108.3282895 109.3179474 110.3076053 111.2972632 112.2869211 113.2765789 114.2662368 115.2558947 116.2455526 117.2352105 118.2248684 119.2145263 120.2041842 121.1938421 122.1835 123.1731579 124.1628158 125.1524737 126.1421316 127.1317895 128.1214474 129.1111053 130.1007632 131.0904211 132.0800789 133.0697368 134.0593947 135.0490526 136.0387105 137.0283684 138.0180263 139.0076842 139.9973421 More 1 2 1 3 6 6 9 12 18 17 26 22 27 47 36 44 47 53 61 60 62 74 70 81 93 73 105 80 88 67 50 56 35 30 19 7 8 5 2Bin
Frequency
Histogram
Frequency 50 55.85714286 61.71428571 67.57142857 73.42857143 79.28571429 85.14285714 More 4 5 7 8 14 10 8 6Bin
Frequency
Histogram
Frequency 75 78.14285714 81.28571429 84.42857143 87.57142857 90.71428571 93.85714286 More 2 5 10 12 14 11 5 3Bin
Frequency
Histogram
Frequency 6 13.14285714 20.28571429 27.42857143 34.57142857 41.71428571 48.85714286 More 1 3 5 6 8 13 9 4Bin
Frequency
Histogram
Frequency 6 13.14285714 20.28571429 27.42857143 34.57142857 41.71428571 48.85714286 More 1 3 5 6 8 11 11 4Bin
Frequency
Histogram
Frequency 3 5.75 8.5 11.25 More 1 3 4 8 4Bin
Frequency
Histogram
Frequency 6 7.75 9.5 11.25 More 1 2 10 5 2Bin
Frequency
Histogram
Frequency 3 5.25 7.5 9.75 More 1 5 8 2 4Bin
Frequency
Histogram
Frequency 3 4.25 5.5 6.75 More 1 3 7 6 3Bin
Frequency
Histogram
Frequency 2 3 4 5 6 7 8 9 10 11 More 1 1 5 13 18 24 18 12 7 2 2Bin
Frequency
Histogram
Frequency 10 35 60 85 110 135 160 185 210 235 260 285 310 335 More 1 1 9 9 17 18 24 27 37 24 21 15 12 4 4Bin
Frequency