Paid days off and the single-sample t test: The number of paid days off (e.g., v
ID: 3303045 • Letter: P
Question
Paid days off and the single-sample t test: The number of paid days off (e.g., vacation, sick leave) taken by eight employees as a small local business is compared to the national average. You are hired as a consultant by the new business owner to help her determine how many paid days off she should provide. In general, she wants to set some standard for her employees, and for herself. Let's assume your search on the Internet for data on paid days off leaves you with the impression that the national average is 15 days. The data for the eight local employees during the last fiscal year are: 10, 11, 8, 14, 13, 12, 12, and 27 days.
h. Consider all the results you have calculated. How would you summarize the situation for this business owner? Identify the limitations of you analyses, and discuss the difficulties of making comparisons between populations and samples. Make reference to the assumptions of the statistical test in your answer.
i. After further investigation, you discover that one of the data points, 27 days, was actually the owner's number of paid days off. Calculate the t statistic and draw a statistical conclusion, adapting for this new information by deleting the value. What changed in the re-analysis of the data?
j. Calculate and interpret the effect size, adapting for this new information by deleting the outlier of 27 days. What changed in the re-analysis of the data?
Explanation / Answer
h. After all the results are calculated. We summarize that for businesss owner that The standard leave days are 15 days as smilar to the national average. He can also provide 15 days paid days leave off to his employees.
But here limitations are
(i) The given sample is too small to provide any suitable result or explaination.
(ii) The sample is taken from internet so not a random sample.
(iii) THe data is of last fiscal year only not for further years, sample not representative of population.
So we cannot say that the given sample is representation of the population.
(i) When we delete the outlier 27 days
the new sample mean = 11.43 days
Standard deviation of the sample (s) = 1.988 days
Test statistic
t = (11.43 - 15)/ (1.988/ sqrt (7) ) = 3.57/ 0.7514 = 4.751
so t (critical for dF = 6) = 1.943
so the result is statistically significant and say the deleting the data changed the scenario completely. Now, we can say that business owner must provide less paid off leaves then national avergae.
(j) Effect size = (New mean - Standard Mean)/ Standard deviation = (11.43 -15)/ 1.988 = 1.80
Which is too much high as compared to earlier effect size of 0.28. In new analysis standard deviation of the sample reduced considerably.
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