3. A clothes manufacturer wishes to find out if adult females have become taller on average since twenty years ago when their mean height was 5 ft 6 inches. Studies over time have shown that the standard deviation of the height of adult females has been fairly constant at 2.3 inches. The manager wishes to test if the mean height is now more than 5 ft 6 inches and takes a sample of 150 adult females.

1. Stating your hypotheses clearly, find the critical region for the mean height of the sample for a test at the \(5 \%\) level of significance. The total height of the females in the sample is 832 ft .
2. Carry out the test making your conclusion clear.