15. 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 in larger families. A sample of n 30 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 50 and a standard deviation of  15. If the mean for the sample is M 58, can the researcher conclude that there is a significant difference in personality between only children and the rest of the population? Use a two-tailed test with  .05.