Question

Test the null hypothesis that the mean difference in the number of cases lost on appeal for the two groups of judges is zero against the alternative hypothesis that the untrained judges lose more cases on appeal. Use an alpha level of .01.

Judge	Untrained	Trained
1	3	0
2	1	3
3	2	4
4	7	4
5	5	2
6	4	5
7	6	1
8	2	1
9	7	0
10	5	6
11	3	4
12	4	2
13	5	5
14	6	3
15	2	1

Paired Samples Correlations

N

Correlation

Sig.

Pair 1

Untrained Judge & Trained Judge

15

.049

.861

Paired Differences

t

df

Sig. (2-tailed)

Mean

Std. Deviation

Std. Error Mean

95% Confidence Interval of the Difference

Lower

Upper

Pair 1

Untrained Judge - Trained Judge

1.40000

2.64035

.68173

-.06218

2.86218

2.054

14

.059

Answer 1

Here, since we need to compare the difference in cases lost between two groups of Judges, it is an independent sample t-test. (It is not a paired sample as it appears since the same judge cannot be trained and untrained!)

Null Hypothesis: The population mean number of cases lost are same for trained and untrained judges.

Alternate Hypothesis: The population mean number of cases lost by untrained judes are more than the trained judges.

Where the index 1 referes to untrained and 2 referes to trained judges.

We need the mean and sd of both the groups.

Judge	Untrained	Trained
1	3	0
2	1	3
3	2	4
4	7	4
5	5	2
6	4	5
7	6	1
8	2	1
9	7	0
10	5	6
11	3	4
12	4	2
13	5	5
14	6	3
15	2	1
Mean	4.133333333	2.73333333
SD	1.922300209	1.90737915

We have here

Level of significance:

Test statistic:

where is the pooled variance.

Substituting the values, we get

The critical value of t at 28 df at 0.01 level of significance =2.7641. (The p-value is 0.0275>0.01) Since the Tcalculated value <TCritical, we do not reject the Null Hypothesis.

Hence we conclude that there is no evidence that the untrained judges lose more cases on appeal.