Question

A city council suspects a judge of being a "hanging judge" because s/he is perceived as imposing harsher penalties for the same sentence. To investigate this, a random sample of 45 cases is taken from the judge's prior cases that resulted in a guilty verdict for a certain crime. The average jail sentence s/he imposed for the sample is 25 months. The average jail sentence for the same type of crimes is 23 months with a standard deviation of 13 months. What can be concluded with α = 0.01?

What is the appropriate test statistic?
---Select--- na

z-test

one-sample t-test

independent-samples t-test

related-samples t-test

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 =  

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

Answer 1

(a)

Question: What is the appropriate test statistic?

Correct option:

z-test

H0: Null Hypothesis: = 23

HA: Alternative Hypothesis: > 23 (Claim)

SE =

= 13/

= 1.9379

Test Statistic is given by:
Z = (25 - 23)/1.9379

= 1.0320

Question: Compute the appropriate test statistic(s) to make a decision about H₀.

Answer : Test Statistic = 1.0320

= 0.01

From Table, critical value of Z = 2.33

Since Test statistic < Critical value, the difference is not significant. Fail to reject H0.

Conclusion:
The data do not support the claim that judge is a "hanging judge" because s/he is perceived as imposing harsher penalties for the same sentence.

From Table, critical values of Z = 2.576

Confidence Interval:

25 (2.576 X 1.9379)

= 25 4.9920

= (20.0080 ,29.9920)

(e)

Effect Size:

(i)

Cohen's d= (25 - 23)/13

= 0.1538

Since d is near 0.2, the effect size is small

(ii)

r² = na