Question

A psychologist is investigating the hypothesis that children who grow up as the only child in the household develop different personality characteristics than those who grow up with at least one sibling. A sample of n = 49 only children is obtained and each child is given a standardized personality test. For the general population, scores on the test from a normal distribution with a mean of µ = 50 and a standard deviation of σ = 15. If the mean for the sample is M = 54, can the researcher conclude that there is a significant difference in personality between only children and the rest of the population?

Answer 1

Solution :

= 50

M =54

=15

n = 49

This is the two tailed test .

The null and alternative hypothesis is ,

H0 :    = 50

Ha :     50

Test statistic = z

= (M  - ) / / n

= (54 - 50 ) / 15 / 49

= 1.87

Test statistic = z = 1.87

P(z >1.87 ) = 1 - P(z < 1.87 ) = 1 - 0.9693

P-value = 2 * 0.0307 =0.0614