Question: Do employees take more sick leave in the year before

Do employees take more sick leave in the year before retirement? They may well have an incentive to do so if their accumulated paid sick leave (the number of days they are entitled to be away with full pay) is about to expire. Indeed, this appears to happen with government workers. One evaluation of this issue looked at statistics gathered by the U.S. General Accounting Office (GAO).21 The study concluded
[What if] the bulge in sick days was just an aberration in the GAO sample rather than a real symptom of goofing off? In zeroing in on this question, we note that the 714 retirees in the GAO sample averaged 30 sick days in their last year instead of the “expected” 14 days. So in a work year of 251 days (average for federal employees), the retirees were finding themselves indisposed 12.0%of the time instead of 5.6%. Could that happen by chance? The science of statistics tells us that the probability of any such swing in so large a sample is low. To be precise, one in 200,000.
a. Identify the population and the sample.
b. Identify the hypotheses being tested, in terms of percent of time indisposed.
c. Identify the p-value here.
d. Which hypothesis (if any) has been rejected? Which has been accepted?
e. How significant (statistically) is the result?

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