A psychologist has developed a standardized test for measuring vocabulary skill for 4­ year­ old children. The scores on the test form a normal distribution with μ = 70 and σ = 20. A researcher would...

A psychologist has developed a standardized test for measuring vocabulary skill for 4­ year­ old children. The scores on the test form a normal distribution with μ = 70 and σ = 20.  A researcher would like to use the test to investigate the hypothesis that children who grow up as an only child develop vocabulary skills at a faster rate than children in larger families.  A sample of n =25 only children is obtained and the mean test score for the sample is M = 77. Perform a two tailed hypothesis test, with an alpha level of .05, and add an APA summary.