A psychologist obtains a random sample of 20 mothers in the first trimester of their pregnancy. The mothers are asked to play Mozart in the house at least 30 minutes each day until they give birth. After 5years, the child is administered an IQ test. It is known that IQs are normally distributed with a mean of 100. If the IQs of the 20 children in the study result in a sample mean of 104.2 and sample standard deviation of 15, is there evidence that the children have higherIQs? Use the =0.05 level of significance.

(a) Determine the null and alternative hypotheses.

H0: = 100

H1: > 100

(b) Calculate theP-value.

P-value =_______

(Round to three decimal places asneeded.)