A city council suspects a judge of being a \"hanging judge\"because s/he is perceived as imposing harsher penalties for thesame sentence. To investigate this, a random sample of 47 cases istaken from the judge's prior cases that resulted in a guiltyverdict for a certain crime. The average jail sentence s/he imposedfor the sample is 26 months. The average jail sentence for the sametype of crimes is 25 months with a standard deviation of 13 months.What can be concluded with an α of 0.05?

a) What is the appropriate test statistic?
---Select--- na z-test one-sample t-test independent-samples t-testrelated-samples t-test

b)
Population:
---Select--- cases same type of crimes city council judge's priorcases months
Sample:
---Select--- cases same type of crimes city council judge's priorcases months

c) Compute the appropriate test statistic(s) tomake a decision about H₀.
(Hint: Make sure to write down the null and alternative hypothesesto help solve the problem.)
critical value =  ; test statistic =
Decision:  ---Select--- Reject H0 Fail to reject H0

d) If appropriate, compute the CI. If notappropriate, input \"na\" for both spaces below.
[  ,  ]

e) Compute the corresponding effect size(s) andindicate magnitude(s).
If not appropriate, input and select \"na\" below.
d =  ;   ---Select--- na trivial effect smalleffect medium effect large effect
r² =  ;   ---Select--- na trivialeffect small effect medium effect large effect

f) Make an interpretation based on theresults.

For the same sentence, the judge imposed significantly harsherpenalties than other judges.

For the same sentence, the judge imposed significantly milderpenalties than other judges.   

For the same sentence, the judge's penalties did notsignificantly differ from other judges.