Question

In: Statistics and Probability

A recent survey of 40 executives who were recently laid off from their previous position revealed...

A recent survey of 40 executives who were recently laid off from their previous position revealed it took a mean of 28 weeks for them to find another position. The sample standard deviation was 6.2 weeks.

a. Construct a 95 percent confidence interval for the population mean.

b. Is it reasonable that the population mean is 31 weeks? Justify your answer.

Expert Solution

Solution :

Given that,

= 28

s =6.2

n =40

Degrees of freedom = df = n - 1 =40 - 1 = 39

a ) At 95% confidence level the t is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2= 0.05 / 2 = 0.025

t /2,df = t0.025,39 = 2.023 ( using student t table)

Margin of error = E = t/2,df * (s / $\sqrt$ n)

=2.023 * (6.2 / $\sqrt$ 40)

= 1.9832

The 95% confidence interval estimate of the population mean is,

- E < < + E

28- 1.9832< <28 + 1.9832

26.0168 < < 29.9832

(26.0168 , 29.9832 )

when take population mean is 31 week

- E < < + E

31- 1.9832< <31+ 1.9832

29.0168 < < 32.9832

(29.0168 ,32.9832)

yes it is reasonable

orchestra answered 2 years ago

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