Question

You know that the US population in 1980 had an average IQ score of 100, with a standard deviation of 1.5. The data records information on 900 young males (26 to 36 years old) from NLSY (the National Longitudinal Surveys), surveys conducted in 1980, show an average IQ score of 101. As a result, you suspect that the young males have a slightly higher average IQ than the population. If the standard deviation of the IQ scores for them is assumed to be the same as the population standard deviation, specifically 1.5, formulate and conduct a hypothesis test to check your suspicions at α = 0.05 significance level.

(A) State your hypothesis test. Explain your choice. Should you assume that the mean IQ score for young males cannot be lower than the US population average?

(B) What statistic would you use? Calculate your observed value.

(C) Identify the rejection regions (in other words, your critical value/values).

(D) Draw your conclusion (inference) based on the relation between the observed and critical values.

(E) What is the p-value of this hypothesis test? What do you conclude based on the p-value?

(F) Construct the associated confidence interval. What is your conclusion for the hypothesis test based on the constructed confidence interval?

Answer 1