A psychologist would like to determine whether there is a relation between depression and aging. It...

A psychologist would like to determine whether there is a relation between depression and aging. It is known that the general population averages μ = 40 on a standardized depression test. The psychologist obtains a sample of n = 9 individuals who are all more than 70 years old. The depression scores for this sample are as follows.

50, 47, 41, 49, 44, 42, 43, 47, 48

On the basis of this sample, can the psychologist conclude that depression for elderly people is significantly different from depression in the general population? Use a two-tailed test at the 0.05 level of significance. (Round your answers to three decimal places.)

t-critical =

Solutions

Expert Solution

H0: = 40

Ha: 40

t critical value at 0.05 level for 8 df is 2.306

From the sample data

= 45.6667

S = 3.2404

Test statistics

t = - / S / sqrt(n)

= 45.6667 - 40 / 3.2404 / Sqrt(9)

= 5.2463

This is test statistics value.

Since Test statistics value > 2.306, we have sufficient evidence to reject H0.

We conclude at 0.05 level that depression for elderly people is significantly different from depression in the

general population.

orchestra answered 1 year ago

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