A social aid office claims that the average score on a self-esteem test for older adults receiving government aid equals 65, with a standard deviation of 5. The test is applied to a random sample of 42 beneficiaries of the help, getting an average score equal to 60. Does this information contradict the welfare office? Use α = 0.05. Solve using the sample distribution approach of sample means.

a)  Solve using the classical approach.

b) Solve using the p-value approach.