Question

A psychologist wants to determine if aging has an impact on depression. 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 67 years old. What can the psychologist conclude with an α of 0.01? The data are below.

id	depression score
2 6 8 12 3 4 11 19 5 6	76.1 44.9 72.5 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--- aging standardized depression test depression elderly general population
Sample:
---Select--- aging standardized depression test depression elderly general population

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

Given that,
population mean(u)=41
sample mean, x =52.27
standard deviation, s =15.4158
number (n)=10
null, Ho: μ=41
alternate, H1: μ!=41
level of significance, α = 0.01
from standard normal table, two tailed t α/2 =3.25
since our test is two-tailed
reject Ho, if to < -3.25 OR if to > 3.25
we use test statistic (t) = x-u/(s.d/sqrt(n))
to =52.27-41/(15.4158/sqrt(10))
to =2.312
| to | =2.312
critical value
the value of |t α| with n-1 = 9 d.f is 3.25
we got |to| =2.312 & | t α | =3.25
make decision
hence value of |to | < | t α | and here we do not reject Ho
p-value :two tailed ( double the one tail ) - Ha : ( p != 2.3118 ) = 0.0461
hence value of p0.01 < 0.0461,here we do not reject Ho
ANSWERS
---------------
a.
Independent-Samples t-test
b.
sample:
aging standardized depression test depression elderly general population
c.
null, Ho: μ=41
alternate, H1: μ!=41
test statistic: 2.312
critical value: -3.25 , 3.25
decision: do not reject Ho
p-value: 0.0461
we do not have enough evidence to support the claim that the general population scores a 41 on a standardized depression test where a higher score indicates more depression
d.
effect size(s) = modulus of (sample mean - population mean)/standard deviation
effect size = modulus of (52.27-41)/15.4158
effect size = 0.7310
medium effect.
e.
The elderly did not significantly differ on depression than the population