Question

Historically, evening long-distance calls phone calls from a particular city have averages 12 minutes per call. In a random sample of 20 calls, the sample mean was 10.7 minutes per call with a standard deviation of 4 minutes. Does the sample indicate a change in the mean duration of long distance calls? Test the hypothesis at 10% level of significance, state the hypothesis and report your conclusion.

a. estimate the p-value and show your work.

Answer 1

given data are:-

sample mean () = 10.7

sample sd (s) = 4

sample size(n) = 20

here, as the sample sd is known and the sample size (n) <30, we will do 1 sample t test for mean.

hypothesis:-

test statistic be:-

df = (n-1) = (20-1) = 19

p value be:-

[ in any blank cell of excel type =T.DIST(-1.453,19,TRUE) press enter]

decision:-

p value = 0.1625 >0.10(alpha)

so, we fail to reject the null hypothesis.

conclusion:-

there is not sufficient evidence to indicate a change in the mean duration of long distance calls at 0.10 level of significance.

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