Question

"Opening up" is thought to improve individuals' mood following a tragic incident. A behavioral therapist is interested in its impact on HIV positive patients. The therapist collected a sample of 24 HIV positive patients and asked them to talk about their HIV related issues ("open up") with their family. The therapist assessed the patients' level of happiness afterwards and obtained a mean of 111.94 with a variance of 22.37. The average happiness of HIV positive individuals is known to be 109. What can be concluded with an α of 0.10?

a) What is the appropriate test statistic?
---Select one--- (na, z-test, One-Sample t-test, Independent-Samples t-test, Related-Samples t-test)
b)
Population:
---Select one--- (individuals' mood, family, HIV positive patients, HIV related issues, HIV positive individuals)
Sample:
---Select one--- (individuals' mood, family, HIV positive patients, HIV related issues, HIV positive individuals)
c) Obtain/compute the appropriate values to make a decision about H₀.
(Hint: Make sure to write down the null and alternative hypotheses to help solve the problem.)
critical value =  ; test statistic =
Decision:  ---Select one--- (Reject H0 or Fail to reject H0)
d) If appropriate, compute the CI. If not appropriate, input "na" for both spaces below.
[  ,  ]
e) Compute the corresponding effect size(s) and indicate magnitude(s).
If not appropriate, input and/or select "na" below.
d =  ;   ---Select one--- (na, trivial effect, small effect, medium effect, large effect)
r² =  ;   ---Select one--- (na, trivial effect, small effect, medium effect, large effect)

f) Make an interpretation based on the results.

a. HIV positive individuals had a significantly worse mood than HIV positive patients that "opened up".

b. HIV positive individuals had a significantly better mood than HIV positive patients that "opened up".    

c. HIV positive individuals did not have significantly different mood than HIV positive patients that "opened up".

Answer 1

(a) One-Sample t-test : The One Sample t Test determines whether the sample mean is statistically different from a known or hypothesized population mean

(b) Population : HIV positive individuals

Sample : HIV positive patients

(c) Ho:

Ha:

Null hypothesis states that HIV positive individuals did not have significantly different mood than HIV positive patients that opened up.

This is a right tailed test as opening up is thought to improve the mood following a tragic incident.

sample mean = = 119.94

variance = 22.37 ; s= 4.73

level of significance = 0.10

The t-critical value for a right-tailed test, for a significance level of α=0.10 ; t critical = tc=1.318

As the t statistics (3.045) falls in the rejection area, we reject the Null hypothesis.  

(d) Find confidence interval.

t value for 90% of confidence interval at 23 df is TINV(0.10,23) = 1.714

Margin of error = E

Confidence interval = Mean +/- E = 109+/-1.655 = (107.35, 110.65)

As 111.94 is not in the range of CI, we reject the Null hypothesis.

(e) Effect size

medium effect.

(f) HIV positive individuals had a significantly worse mood than HIV positive patients that "opened up"