The 40-hour workweek did not become an American standard until 1940. Today, many

Question

The 40-hour workweek did not become an American standard until 1940. Today, many white-collar employees work more than 40 hours per week because management demands longer hours or offers monetary incentives. The mean and standard deviation of the number of hours worked in a random sample of 14 white-collar employees are 44.39 and 3.38, respectively. Is there any evidence that the true mean number of hours worked by white-collar employees is greater than 40? Justify your answer by conducting a test of the appropriate hypotheses at significance level 0.01. State any assumptions that you have made.

Explanation / Answer

we are assuming that sample is normally distributed as well randomely chosen

null hypothesis:Ho:mean =40

alternate hypothesis:Ha: mean >40

at 0.01 level of significance and 13 degree of freedom ; critical value t=2.6503

decision rule; reject Ho: if t>2.6503

for std error of mean =std deviation/(n)1/2 =0.9033

test stat z=(X-mean)/std error =(44.39-40)/0.9033 =4.8597

as test stat is higher then critical value we reject null hypothesis and conclude that the true mean number of hours worked by white collar employee is greater then 40.

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