Question

A psychologist hypothesizes that depression decreases with aging. It is known that the general population scores a 41 on a standardized depression test where a higher score indicates more depression. The psychologist obtains a sample of individuals that are all over 65 years old. What can the psychologist conclude with an α of 0.05? The data are below.

id	depression score
2 6 8 12 3 4 11 19 5 6	76.1 44.9 64.8 42.2 30.1 67.6 51.3 36.5 54.3 47.2

a) What is the appropriate test statistic?
---Select--- na z-test One-Sample t-test Independent-Samples t-test Related-Samples t-test

b)
Population:
---Select--- elderly standardized depression test general population depression aging
Sample:
---Select--- elderly standardized depression test general population depression aging

c) Compute the appropriate test statistic(s) to make a decision about H₀.
(Hint: Make sure to write down the null and alternative hypotheses to help solve the problem.)
p-value =  ; Decision:  ---Select--- Reject H0 Fail to reject H0

d) Using the SPSS results, compute the corresponding effect size(s) and indicate magnitude(s).
If not appropriate, input and/or select "na" below.
d =  ;   ---Select--- na trivial effect small effect medium effect large effect
r² =  ;   ---Select--- na trivial effect small effect medium effect large effect

e) Make an interpretation based on the results.

The elderly are significantly more depressed than the population.

The elderly are significantly less depressed than the population.    

The elderly did not significantly differ on depression than the population.

Answer 1

Let denotes the average score on a standardized depression test.

a) The appropriate test statistic - One-Sample t-test

b) Population - general population

Sample - elderly

c)

d) The effect size is , large effect

e) The elderly are significantly more depressed than the population.