a hypothesis test is a comparison of before and after data on a group of student
ID: 3360648 • Letter: A
Question
a hypothesis test is a comparison of before and after data on a group of students who received training to improve their grades in statistics. Their pre- and post- scores on a statistics test are given below.
ID Before After
1 65 75
2 70 78
3 80 78
4 54 67
5 62 61
6 77 77
7 74 81
8 83 86
Paired Samples Statistics
Mean
N
Std. Deviation
Std. Error Mean
Pair 1
Before
70.6250
8
9.82617
3.47407
After
75.3750
8
7.90908
2.79628
Paired Samples Correlations
N
Correlation
Sig.
Pair 1
Before & After
8
.826
.012
Paired Samples Test
Paired Differences
t
df
Sig. (2-tailed)
Mean
Std. Deviation
Std. Error Mean
95% Confidence Interval of the Difference
Lower
Upper
Pair 1
Before - After
-4.75000
5.54849
1.96169
-9.38865
-.11135
-2.421
7
.046
(13) What type of t test (one sample, two independent samples, or paired samples) is appropriate for this comparison? Is it a one-tailed or a two-tailed test?
(14) What are the null and alternative hypotheses?
(15) What are the n, the mean and standard deviation before training, and the mean and standard deviation after training? What do these results suggest about the effect of the training?
(16) What is the result of the t-test? Is it statistically significant at .05? (How will you need to adjust the p-value to your output?) What do you conclude about the original hypothesis?
(17) What does the 95% Confidence Interval estimate show about the mean difference in test scores before and after training? In what way is it consistent with the result of the hypothesis test?
Paired Samples Statistics
Mean
N
Std. Deviation
Std. Error Mean
Pair 1
Before
70.6250
8
9.82617
3.47407
After
75.3750
8
7.90908
2.79628
Explanation / Answer
13) It is a paired 2 sample t test
It is a two tailed test.
14)
Null: Before and after training scores are same
Alt: Before and after training scores are different
15) Before:
Before
70.6250
8
9.82617
n = 8, mean = 70.625, SD = 9.82617
After:
After
75.3750
8
7.90908
16) p value from t test = 0.046
p < alpha (0.05)
Thus, null is rejected
Which means before and after training scores are different.
17) If repeated samples were taken and the 95% confidence interval was computed for each sample, 95% of the intervals would contain the population mean. A 95%confidence interval has a 0.95 probability of containing the population mean. 95% of the population distribution is contained in the confidence interval.
Interval does not contain 0, thus null is rejected ansd we can say that means before and after training scores are different.
Before
70.6250
8
9.82617
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