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 minutes 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 in the study 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=0.10 level of significance.

P value =

Answer 1

Solution :

= 100

=104.4

s =15

n = 20

This is the right tailed test .

The null and alternative hypothesis is ,

H0 :    = 100

Ha : > 100

Test statistic = t

= ( - ) / s / n

= (104.1-100) / 15 / 20

= 1.312

Test statistic = t =1.312  

P-value =0.1094

= 0.05  

P-value >

0.1094 > 0.05

Do not reject the null hypothesis .

There is insufficient evidence to suggest that