Question

A factory manufactures cellphone batteries that have a duration that is distributed in an approximately normal way with a mean of 800 hours and a standard deviation of 40 hours. A random sample of 30 batteries has a mean duration of 785 hours.

a) Does that data show enough evidence to say that the mean duration is less than 800 hours? Use a significance level of 5%

b) What is the probability of saying that the mean is of 800 hours when in reality it is of 780 hours?

Answer 1

a)


The test hypothesis is

This is a left-tailed test because the alternative hypothesis is formulated to detect claim if mean is less than 800.0.
Now, the value of test static can be found out by following formula:

OR

b)
The probability (= 0.005) of saying that the mean is of 800 hours when in reality it is of 780 hours