number of paid days orf taken by eight employees ata asmall Putting It All Toget

Question

number of paid days orf taken by eight employees ata asmall Putting It All Together 9.50 Paid days off and the single-sample t test: The umber of paid days off e.g., vacation, sick leave) taken y cight employees at 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. a. Write hypotheses for your research. b. Which type of test would be appropriate to analyze these data in order to answer your question? c. Before doing any computations, do you have any concerns about this research? Are there any ques- tions you might like to ask about the data you have been given? Calculate the appropriate t statistic. Show all of your work in detail. d. e. Draw a statistical conclusion for this business owner. f. Calculate the confidence interval. g. Calculate and interpret the effect size. h. Consider all the results you have calculated. How would you summarize the situation for this business

Explanation / Answer

a. Hypothesis:

Ho: mu = 15

vs

H1: mu is not equals to 15

mu = national population average

b. T test will be appropriate to test the hypothesis. Because here, we can find sample mean and sample sd. and the sample size is less than 30.

d. sample mean = xbar = sum of (10,11,8,14,13,12,12,27) / 8

= 13.375

sample size = n = 8

sample sd=s= 5.804862

t statistic:

t = (xbar-mu)/ [s/sqrt(n)] =  -0.7917834

f. 95% Confidence Interval: 13.375 ± 4
(9.375 to 17.375)

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