Arecent survey of 50 executives who were laid off during a recent recession revealed it took a mean of 26 weeks for them to find another position. the standard deviation of the sample was 6.2 weeks. construct a 95% confidence interval for the population mean. is it reasonable that the population mean is 28 weeks? justify your answer.

Formula to find the confidence interval for population mean :-

, where = sample mean.

t*= critical z-value

n= sample size.

s= sample standard deviation.

By considering the given question , we have

n= 50

Degree of freedom : df = 49  [ df=n-1]

Significance level :

Using students's t-distribution table, the critical t-value for 95% confidence =

Then,  95% confidence interval for the population mean will be :

Hence, a 95% confidence interval for the population mean = (24.24, 27.76)

Since 28 is not contained in the above confidence interval , it means it is not reasonable that the population mean is 28 weeks.

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