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...

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 μ = 50 and a standard deviation of σ = 15. If the mean for the sample is M = 58, (Use α = .05) Can the researcher conclude that there is a significant difference in personality between only children and the rest of the population? Please show all computational processes that lead your answer and all four steps including alpha level, critical z-scores, critical region, and normal distribution of hypothesis testing.