Statistics Homework

Instructions

  Directions: All answers are to be contained in one excel file. Please do not delete this tab (the instructions tab). This is an open book, open notes exam. The one limitation is that you may not work with other people. This test must be completed independently. Be sure your name is on your document. Good luck!

Q1

Q1. What is the risk of performing the t-test using pooled variance, if the variances between the two samples are actually unequal (i.e. fail the F test)? (Select the correct answer from the choices below.) A. You will fail to adjust for sample size. B. You may falsely accept or reject the null hypothesis. C. Your result will only be applicable for a one-tail t-test.

Q2

Q2. Which measure of central tendency can be used for both numerical and categorical variables? (Select the correct answer from the choices below.) A. Median B. Geometric Mean C. Mode D. Arithmetic Mean  

Q3

Q3. The probability that a new advertising campaign will increase sales is assessed as being 0.80. The probability that the cost of developing the new ad campaign can be kept within the original budget allocation is 0.40. Assuming that the two events are independent, the probability that the cost is kept within budget and the campaign will increase sales is: (Select the correct answer from the choices below.)   A. 0.32 B. 0.68 C. 0.88 D. 0.20

Q4

The age distribution of students at a community college is given below:

Suppose a student is selected at random. Let A = the event the student is under 21 B = the event the student’s age is between 21 and 25 C = the event the student’s age is between 26 and 30 D = the event the student’s age is between 31 and 35 E = the event the student’s age is 35 and under

Q5

Q5: Statistical significance can be determined from descriptive statistical analysis alone? (Select the correct answer from the choices below.) A. True B. False

Q6

Q6. Refer to the tab titled "thrombosus data" for data required to solve this problem. You are looking at patients supported by a Left Ventricular Assist Device (LVAD). Within this patient group, you have Group No (those who have not had a thrombus event) and Group Yes (those who have had a thrombus event). A thrombus event is an event in which a blood clot developed in the LVAD. Data has been sorted in the tab "Thrombus Event" to list "No" thrombus event patients first. In addition, you have data related to time (in days) that the patient has been supported by the LVAD. You'd like to know if patients in Group No have been supported for the same amount of time on their LVADs as those in Group Yes. You believe that the longer a patient is supported by an LVAD , the more likely the patient is to have a thrombus event. Therefore, you want to show statistically that Group Yes has a longer average time spent on the LVAD. You will need to answer the questions below to see what the results actually show. Answer questions 1 through 5 below.

#1. What is your null hypothesis (H0) for this research topic? (Select either A or B from below.) A. There is no difference in days supported by an LVAD between Group No and Group Yes. B. Group Yes patients have been supported by an LVAD for more days than Group No patients.

#2. Calculate the average time (in days) supported by an LVAD for each group. (Use Excel formula.) A. ______ days for Group No B. ______ days for Group Yes

#3. Calculate the variance for time (in days) supported by an LVAD for each group. (Use Excel formula.) A. ______ days for Group No B. ______ days for Group Yes

#4. What is the sample size (n) for each group? A. ______ Group No B. ______ Group Yes

#5. Perform the appropriate statistical test to test for significance between the the two groups. Note, you can use the "data analysis toolpak" to get your result. You will need to format the data to be able to run the analsysis. Based on your results: A. What p-value did you find? B. Describe what your findings mean. Is there a significant difference between the groups? C. Would you accept or reject the null hypothesis?

Q7

Q7. Which words can be used to describe quantitative research methods? (Select all that apply.) A. Words B. Numbers C. Structured D. Randomly selected samples E. Focus is on the research subject's view F. Objective

Q8

Q8. A medical device manufacturer claims to have developed a thin AICD that contains a mean of no less than 41 Joules of stored energy. From previous studies, it is believed that stored energy for AICDs is normally distributed with a standard deviation of 2 Joules. A consumer group has decided to try to discover if the claim appears true. They take a sample of 20 AICDs and find that the mean of stored energy is 40.6 Joules.   Referring to the information above, the appropriate hypotheses to determine if the manufacturer's claim appears reasonable is:   A. H0: μ ≥ 41 versus H1: μ < 41 B. H0: μ > 41 versus H1: μ ≠ 41 C. H0: μ ≤ 41 versus H1: μ > 41 D. H0: μ ≥ 40.6 versus H1: μ < 40.6

Q9

Q9. Refer to the tab titled "Tobacco Use" for data required to solve this problem. The premise of this problem is that you are looking at a group of patients with heart failure. Patients either have ischemic cardiomyopathy (ICM) or non-ischemic cardiomyopathy (NICM). You have gathered information about their smoking history. You are wondering if there is a relationship between these 2 variables (i.e. type of heart disease and history of tobacco use). (Ischemic cardiomyopathy is a result of plaque buildup in vessels.) Answer questions 1 through 5 below.

#1. What type of variables do you have? Numerical or Categorical? A. Type of heart disease is a __________________ variable. B. History of smoking is a ___________________ variable.

#2. Which of the two variables is the independent variable (type of heart disease or history of smoking)?

#3. If you were to test the relationship between the 2 variables, which inferential statistical test would you use?

#4. What would your hypotheses be? A. The null hypothesis (H0) would state: _______ B. The alternative hypothesis (H1) would state: _________

#5. Setup a contingency table for this problem in the table below. Label all 4 categories in the fields that state "category title". Enter the counts in the fields that state "count". Calculate the totals for each field that states "total".

Q10

Q10. Refer to the tab titled "Financial Data" for data required to solve this problem. This data represents financial data associated with 4 different types of readmissions. Use the column titled "Cause of Readmission" and the column titled "Contribution Margin" to answer the following questions. Answer questions 1 through 4 below.

#1. Calculate the mean of the contribution margin for each of the 4 categories under "cause for readmission". (Use Excel formula.) A. Stroke: mean = ______ B. GI Bleed: mean = ______ C. Other: mean = ______ D. Vtach &/or AICD Fire: mean = ______

#2. Construct a column chart that shows the means of the 4 groups. Label the chart appropriately.

#3. Using 95% CI, calculate the upper and lower confidence limits for the "contribution margin" data for the category "other". Assume t-distribution.

#4. Describe the meaning of the confidence limits that you just calculated.

Q11

Q11. This question is related to simple linear regression. In simple linear regression, the goal is to determine if there is a linear change in the _______ variable based on a change in the ______ variable. The dependent variable will always be a ________ variable. If a negative relationship is found, this means that as the independent variable _______, the dependent variable _______. (Select the correct answer from the choices below to correctly fill in the blank words.) A. dependent, independent, categorical, increases, decreases B. independent, dependent, categorical, increases, decreases C. independent, dependent, categorical, decreases, increases C. dependent, independent, numerical, increases, decreases D. dependent, independent, numerical, decreases, increases E. independent, dependent, numerical, decreases, increases

Q12

Q12. Refer to the tab titled "Financial Data" for data required to solve this problem. This data represents financial data associated with 4 different types of readmissions. Use the column titled "Cause of Readmission" and the column titled "Length of Stay" to answer the following questions. Answer questions 1 through 5 below.

#1. Arrange the data in a format so that you can perform a one-way ANOVA to test for significant difference in Length of Stay between the 4 causes for readmissions.

#2. What is an appropriate null hypothesis (H0)for this data analysis?

#3. Perform a one-way ANOVA to test for significant difference in Length of Stay between the 4 causes for readmissions. (It is recommended that you use the data analysis toolpak addin to perform the test.)

#4. Based on the F statistic from your ANOVA test, woul d you accept or reject your null hypothesis? Explain why.

#5. Based on the p-value from your ANOVA test, woul d you accept or reject your null hypothesis ? Explain why.

Q13

Q13. According to the empirical rule, if the data form a "bell-shaped" normal distribution, what percent of the observations will be contained within 3 standard deviations around the arithmetic mean. (Select the correct answer from the choices below.) A. 68.26 B. 95.0 C. 75.00 D. 99.7

Q14

Q14: Match the appropriate inferential statistical test to the provided definitions.

A. Chi-Square Test B. ANOVA C. t-test

1. Used to test independence for more than 2 means (i.e. compares the means of more than 2 groups) Letter: _______ 2. Used to test the independence between 2 or more categorical variables Letter: _______ 3. Used to compare means of 2 groups Letter: _______

Thrombus Event

Tobacco Use

Financial Data