Question

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 min each day until they give birth. After 5​ years, 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 result in a sample mean of 104.4 and sample standard deviation of 15, is there evidence that the children have higher​IQs? Use the α=0.05 level of significance.

A) Determine null and alt hypotheses

H0: ____ _____ 100

H1: ____ ______ 100

B) Calculate p value

C) State conclusion. Reject or not? Sufficient evidence at .05 level of significance that mothers who listen to Mozart have kids with higher IQs?

Answer 1

Solution :

Given that,

Population mean = = 100

Sample mean = = 104.4

Sample standard deviation = s = 15

Sample size = n = 20

Level of significance = = 0.05

This a right (One) tailed test.

A)

The null and alternative hypothesis is,  

Ho: 100

Ha: 100

The test statistics,

t = ( - )/ (s/)

= ( 104.4 - 100 ) / ( 15 / 20)

= 1.312

df = n - 1 = 19

B)

P- Value = 0.1026

C)

The p-value is p = 0.1026 > 0.05, it is concluded that the null hypothesis is fails to reject.

It is concluded that the null hypothesis is fails to reject, Therefore, there is not sufficient evidence at 0.05 level of significance

that mothers who listen to Mozart have kids with higher IQs