1. A school publicizes that the proportion of its students who are involved in extracurricular activities is 61%. A board member thinks that this percentage is too high so asks for help to determine whether this is true.

We will test the hypotheses

H0: p = 0.61

Ha: p < 0.61

A sample of 75 students gave 55% who were involved in extracurricular activities. A significance test gives a P-value of 0.025. Interpret this value in the context of the problem.

Make a conclusion based on the P-value.

2. A company advertises that the mean life of its furnaces is more than 18 years Solution:

State the hypotheses

H0: = 18

Ha: > 18

35 customers are randomly selected and it is found that the average furnace life for the sample was 20 years. A significance test gives a P-value of 0.112. Interpret this value in the context of the problem.

Make a conclusion based on the P-value.