Question

A school psychologist wants to know if a popular new hypnosis technique impacts depression. The psychologist collects a sample of 14 students and gives them the hypnosis once a week for two months. Afterwards the students fill out a depression inventory in which their average score was 43.04. Normal individuals in the population have a depression inventory average of 49 with a variance of 144.00. What can the psychologist conclude with an α of 0.01?

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--- normal individuals two months students receiving hypnosis depression new hypnosis technique
Sample:
---Select--- normal individuals two months students receiving hypnosis depression new hypnosis technique

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.)
critical value =  ; test statistic =
Decision:  ---Select--- Reject H0 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 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

f) Make an interpretation based on the results.

The depression of students that underwent hypnosis is significantly higher than the population.

The depression of students that underwent hypnosis is significantly lower than the population.    

The depression of students that underwent hypnosis is not significantly different than the population.

Answer 1

a) What is the appropriate test statistic?

Since, we know the population variance, we will use
z-test

b)
Population:
normal individuals
Sample:
two months students receiving hypnosis depression new hypnosis technique

c) Compute the appropriate test statistic(s) to make a decision about H₀.
H₀ : Mean depression of students that underwent hypnosis is equal to that of normal students.

H_a : Mean depression of students that underwent hypnosis is less than that of normal students.
α of 0.01 critical value = -2.326 ;

Standard error of sample mean = = 3.207135

test statistic z = (43.04 - 49) / 3.207135 = -1.858356

Since the test statistic is not less than -2.326 and hence does not fall in the critical region, we fail to reject H0.
Decision: Fail to reject H0

d) If appropriate, compute the CI. If not appropriate, input "na" for both spaces below.

Lower limit = 49 - 2.326 * 3.207135 = 41.5402

Upper limit = 49 + 2.326 * 3.207135 = 56.4598
[ 41.5402 ,  56.4598]

e) Compute the corresponding effect size(s) and indicate magnitude(s).
If not appropriate, input and select "na" below.
d = |43.04 - 49|/ = 0.4967

Since, d lies between 0.20 and 0.50 it is small effect
r² =  ;   na

f) Make an interpretation based on the results.

Since we fail to reject H0,

The depression of students that underwent hypnosis is not significantly different than the population.