Graduate Level Statistics

Statistics

Name of the Student

Instructor

Institution

Course

Date

1. Hypothesis testing is used to analyze an assumption that is made about a particular parameter in a population. It is a means of establishing the validity of the achieved results. The main reason why hypothesis testing is carried out in statistical analysis is to infer the results of the formulated on a particular data sample (Diehl & Williams, 2017). During analysis, an individual formulates the null and the alternative hypothesis. However, these are speculations of the characteristics exhibited by a particular parameter in the population. Therefore, to understand which of the characteristics is true, it is important to test the hypothesis. When the null hypothesis is true then it is accepted. However, when it is not true then it is rejected. Without performing hypothesis testing, it is thus impossible to make the right inferences in a population(Diehl & Williams, 2017). Statistical inferences aid in analyzing data which facilitates the interpretation of research results as well as drawing conclusions. For this reason, in all samples collected in a population it is important to formulate a hypothesis, develop an analysis plan, test it, and make proper interpretations.

2. The second reason why hypothesis testing is important to carry out hypothesis tests in statistical analysis is so as to justify the conclusions made without using scientific theories that exist(Diehl & Williams, 2017). As a result, it is an effective way especially for use in discerning the effect that one factor has on another through exploration of the statistical significance relationships. However, when Bayesian hypothesis testing is carried out, it is possible to determine whether the results that were obtained from a test can be repeated. Repeating any scientific research could be due to the failure of the researchers to take into consideration some of the aspects within the study. For this reason, the results obtained are biased(Diehl & Williams, 2017). This cannot be determined until a hypothesis testing is carried out. Therefore, performing hypothesis testing at the stage of statistical analysis helps the researcher to understand the validity of the process. When the results differ from either existing ones or theories then more effort is needed to repeat the entire collection and analysis of the statistical data.

3.

a. The normal curve is a graph that is used to visualize delineation of frequency and probabilities of a data set (Wilcox, 2017). The normal curve helps one to understand the performance of Emily against the other students. This is because it shows the percentage of children who have earned either high or low scores. When all the scores of the children in a class are plotted on the graph then a bell shape is formed. Most of the children perform averagely and this is the reason why the normal curve is highest in the middle. However, to determine the scores of Emily which is one standard deviation above the mean, it means that she scored above the average.

b. From the information, Emily scored one standard deviation above the mean. Therefore, determining the percentile rank will help understand the exact performance in relation to the class. Therefore, her rank is 84% (Bishara&Hittner, 2017). As a result, she scored equally or higher than 84% of the class. Those who scored lower are thus lower than this rank

c. Those who scored higher than Emily are 100-84= 16% of the class.

4. From the scenario, it is said that more than 30% of mole biopsies are unnecessary. This can be taken to mean that one can estimate that in every sample more than this percentage of the moles will have benign results. In this case one tail test will be used to test the hypothesis. This is because the critical area of distribution is one sided (Kock, 2015). In this case it is greater than 30%. Therefore, one tailed statistical test in this case will be used to show that the sample mean would be higher than the population mean. Therefore, the direction of interest is single whereby only the results showing higher sample mean is necessary. In this case, H0: μ≤ 30%. H1: μ>30%. From the dermatologist’s results, 210 out of 634 cases were benign. This is gives 33.1% of the moles which had benign results. In this case, the results are greater than hypothesized value. As a result, the null hypothesis is false and hence the alternative hypothesis is not rejected. As such, the dermatologist’s claim cannot be rejected.

5.

Gender

In this dataset, there are a total of 50 individuals in which 26 are females and 24 are males. This means that the males constitute 52% of the study group. The males are 48%. The mean value is 1.52;median and mode are both 2. This means that the females occur more in the dataset as compared to males.

Age

The mean, median and modal ages for the employees are 32.02, 31.5, and 29 respectively. Therefore, the average age for the employees is 32 and the most occurring age is 29. The range in the dataset is 15 which is the difference between the highest and lowest ages.

Relationship with Supervisor

The average relationship with the supervisor is 2.5. This is between neutral and positive relationship. However, most of the employees have a positive relationship with the supervisor because the modal value is 3. As such, the supervisors and the employees relate and coordinate well.

Telecommute Schedule

The average telecommute value is 1.18. The modal value is 1. This means that the average value is more on value 1 which is no ability to telecommute. The same case applies to the modal value where majority of the employees have no ability to telecommute. The employees therefore, mostly work from the office as opposed to working at home using emails or internet.

Relationship with Coworkers

The average value of relationship with coworkers is 1.92. This means that on average the employees have no relationships amongst each other. The modal value is 2 meaning showing that the employees establish no relationships in the working place. They also do not have a negative working relationship. This means that the employees greatly work on their own projects as opposed to collaborating.

Workplace Happiness

Happiness in the workplace is determined by several factors. The average happiness value in the organization is 7.4. This means that the employees have no happiness. On overall, there is no employee in the entire department who is completely happy. A value of seven is registered as the mode which shows employees at work are not happy.

Workplace Engagement

Workplace engagement determines the employees’ ability to give their best on a daily basis. In this case on average, the workers are engaged at a level of 7.64. This means that there is no engagement. All of them are involved in activities but their full potential is not exploited. The mode is 8 which is an indication of no engagement at work.

Overall Combined Rating

On overall, the average combined rating is 15.02. This shows that the employees are not happy and at the same time not engaged. This means that the employees perform poorly in the organization as a result of lack of happiness. The modal value is 15. This means still majority of the employees lack to be fully engaged in their work and they are not happy.

Excel output

References

Bishara, A. J., &Hittner, J. B. (2017).Confidence intervals for correlations when data are not normal. Behavior research methods, 49(1), 294-309.

Diehl, S. J., & Williams, F. R. (2017). Statistical methods for hypothesis testing and benchmarking: Applications in route prioritization and beyond (No. 17-00231).

Kock, N. (2015). One-tailed or two-tailed P values in PLS-SEM?. International Journal of e-Collaboration (IJeC), 11(2), 1-7.

Wilcox, R. (2017). Modern statistics for the social and behavioral sciences: A practical introduction. Chapman and Hall/CRC.