Question

A researcher suspected that age is related to depression. It is known that the general population average μ=40 on a standard depression test. The researcher obtained a sample of individuals who are more than 75 years old. The depression score of this sample are as follows: 48, 38, 42, 48, 39, 47, 41, 42, 42. On the basis of this sample, is depression for elderly people significantly different from depression in the general population at α=0.05 level?

1. 1) State the hypothesis (H0 and H1) for the two-tailed test.

2. 2) Did the sample support researcher’s hypothesis? Show the process for your decision.

3. 3) Later, the researcher knew that the standard depression test has σ=5, would that

   change the conclusion? Show the process for your decision.

Answer 1

The sample mean and sample standard deviation is

1) Define the null and the alternative hypothesis as

2) We use to test as sample is of small size and population standard deviation not given

The value of test static

The test is two tailed and number of degrees of freedom is 9-1=8

So, p-value is

As 0.0446<0.05

Reject the null hypothesis, Yes, the sample support researcher’s hypothesis.

3) Using standard deviation 5, we have the value of test static as

So p-value is

As 0.1096>0.05

We fail to reject null hypothesis.

In this case the sample does not support researcher’s hypothesis?