Question

For many years, "working full-time" has meant working 40 hours per week. Nowadays it seems that corporate employers expect their employees to work more than this amount. A researcher decides to investigate this hypothesis. The null hypothesis states that the average time full-time corporate employees work per week is 40 hours. The alternative hypothesis states that the average time full-time corporate employees work per week is more than 40 hours. To substantiate his claim, the researcher randomly selected 250 corporate employees and finds that they work an average of 47 hours per week with a standard deviation of 3.2 hours. In order to assess the evidence, what do we need to ask?

Answer 1

How likely it is that in a sample of 250 we will find that the mean number of hours per week corporate employees work is as high as 47 if the true mean is 40

Explanation:

Answer 2

Explanation:

`H_0:  xbar =40\\H_a: x bar >40`

(One tailed test)

Sample size n =250

x bar = sample mean =47

Mean difference =47-40 =7

Std dev =3.2 hours

Std error =
`(3.2)/(\sqrt 250  ) =0.453`

Since population std dev not known t test to be used

t statistic = mean diff/stderror =
`(7)/(0.453) =15.452`

df = 31

p value =0.000

p<Alpha

Hence there is evidence to prove that working hours exceed 40 hours.