Let be the population mean .
By observing the given information, we have :-
Since the alternative hypotheses is two tailed so the test is a two-tailed test.
We assume that the life of a large shipment of CFLs is normally distributed.
(a) Given : Sample size : n=81 , since n>30 so we use z-test.
Sample mean :
Standard deviation :
Test statistic for population mean :-
The critical value (two-tailed) corresponds to the given significance level :-
Since the observed value of z (-1.4) is less than the critical value (1.96) , so we do not reject the null hypothesis.
Hence, we conclude that we have enough evidence to accept that the mean life is different from 7450 hours .
(b) The p-value : , it means that the probability that the life of CFLs less than 7240 and greater than 7240 is 0.1615.
(c) The confidence interval for population mean is given by :-
,