Question

A sociologist wants to know about the stress levels in the nation over the past years. In the late 2000s, the average score on the Brown's Stress Inventory (BSI) in the nation was 19 with a standard deviation of 6.6. A current day sample of 30 produces a mean BSI score of 18.4. What can the sociologist concludes 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--- current sample the nation the years stress levels the BSI score
Sample:
---Select--- current sample the nation the years stress levels the BSI score

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.

There has been a significant increase in depression over the years.There has been a significant decrease in depression over the years.    There has been no significant change in depression over the years.

Answer 1

(a)

the appropriate test statistic : z-test

(b)

Population: the nation

Sample: current sample

(c)

H0: Null Hypothesis: = 19

HA: Alternative Hypothesis: 19

= 0.01

From Table:

critical values of Z = 2.576

SE = /

= 6.6/

= 1.2050

Test statistic is given by:
Z = (18.4 - 19)/1.2050

= - 0.4979

Since calculated value of Z = - 0.4979 is greater than critical value of Z = - 2.576, difference is not significant. Fail to reject null hypothesis.

Conclusion:
The data do not support the claim that the average score on the Brown's Stress Inventory (BSI) in the nation is different from 19.

(d)

= 0.01

From Table:

critical values of Z = 2.576

Confidence Interval:

18.4 (2.576 X 1.2050)

= 18.4 3.1041

= [ 15.2959 , 21.5041]

(e)

Since d is less than 0.1, trivial effect.

Thus, answer is:

d = 0.0909, trivial effect

r² = na

(f)

Correct option:

There has been no significant change in depression over the years.