15.51 To characterize precisely how many sick days its employees take, a random sample of 50 employee ﬁles was selected and the following statistics were determined: x¯ = 9.50 days and s2 = 42.25. (i) Determine a 95% conﬁdence interval on μ, the true population mean number of sick days taken per employee. (ii) Does the evidence in the data support the hypothesis that the mean number of sick days taken by employees is less than 14.00 days? (iii) What is the power of the test you conducted in (ii). State any assumptions clearly. (iv) The personnel director who ordered the study was a bit surprised at how large the computed sample variance turned out to be. However, the human resources statistician insisted that this is not necessarily larger than the typical in- dustry value of σ2 = 35. Assuming that the sample is from a normal population, carry out an appropriate test to conﬁrm or refute this claim. What is the p-value associated with the test?
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