Question

# Suppose that the national average population mean score on a Depression index taken one year after...

Suppose that the national average population mean score on a Depression index taken one year after a traumatic event is 71.4. A psychologist takes a random sample of 90 patients who have been receiving a new type of therapy in response to a traumatic event. Their scores on the Depression index taken one year after the traumatic event have a sample mean of 65.2 and a sample standard deviation of 14.8. Does the population mean Depression index score for patients receiving the new therapy differ from national average? Conduct a hypothesis test with α=.05. Show all work.

Can you also explain how you got the p value

=71.4, n=90, = 65.2, s=14.8, =0.05

Ho: = 71.4

H1: 71.4

Formula for test statistics is

t= -3.9742

now calculate t critical value using t table with

Df= n-1 = 90-1=89 and =0.05

We get critical value as

Critical value= (-1.987, 1.987)

Now we observe that,

(Test statistics=-3.9742) < (critical value= -1.987)

Thus, test statistics lies in rejection region

Hence we reject null hypothesis.

Therefore there is sufficient evidence to claim that the mean Depression index score for patients receiving the new therapy differ from national average.