13) A psychologist would like to test whether there is a relationship between depression and aging. For the general population of adults, it is known that the mean depression test score is 40 with a standard deviation of 10. It is also known that the depression test scores follow normal probability distribution. He took a random sample of 28 individuals who are older than 70 years of age. The average depression test score of this sample is 43.5.

a) Set up your null and alternative hypotheses to test the claim the elderly people are more depressed.

b) Compute the value of the test statistic. Round to two decimal places.

c) What is your p-value? Give four decimals.

d) What is your conclusion at 0.05 significance level? Write clearly whether you have evidence to support the claim.

e) If the psychologist wanted to test whether depression for elderly people is significantly different from the depression in the general population, what is his alternative hypothesis?

f) What is the conclusion at 0.05 significance level? Can he conclude that the elderly people are significantly different from general population regarding depression?