In an effort to improve the mathematical skills of 17 students, a teacher provides a weekly 1-hour tutoring session. A pre-test is given before the sessions and a post-test is given after. The results are shown here. Test the claim that there was an increase in the scores. at αα=0.01. You believe that the population is normally distributed, but you do not know the standard deviation. When calculating difference use Post-test minus Pre-test. pre-test post-test 77 71 48 53 68 61 59 54 75 76 65 73 50 57 100 106 55 61 98 91 85 92 51 53 75 81 88 97 57 52 70 77 55 64 Which of the following are the correct hypotheses? H0:μd≥0H0:μd≥0 HA:μd<0HA:μd<0(claim) H0:μd≤0H0:μd≤0 HA:μd>0HA:μd>0(claim) H0:μd=0H0:μd=0 HA:μd≠0HA:μd≠0(claim) Given that αα is 0.01 the critical value is 2.584 The test statistic is: (round to 3 places) The p-value is: (round to 3 places) The decision can be made to: reject H0H0 do not reject H0H0 The final conclusion is that: There is enough evidence to reject the claim that there was an increase in the scores. There is not enough evidence to reject the claim that there was an increase in the scores. There is enough evidence to support the claim that there was an increase in the scores. There is not enough evidence to support the claim that there was an increase in the scores.
In an effort to improve the mathematical skills of 17 students, a teacher provides a weekly 1-hour tutoring session. A pre-test is given before the sessions and a post-test is given after. The results are shown here. Test the claim that there was an increase in the scores. at αα=0.01. You believe that the population is
| pre-test | post-test |
|---|---|
| 77 | 71 |
| 48 | 53 |
| 68 | 61 |
| 59 | 54 |
| 75 | 76 |
| 65 | 73 |
| 50 | 57 |
| 100 | 106 |
| 55 | 61 |
| 98 | 91 |
| 85 | 92 |
| 51 | 53 |
| 75 | 81 |
| 88 | 97 |
| 57 | 52 |
| 70 | 77 |
| 55 | 64 |
Which of the following are the correct hypotheses?
- H0:μd≥0H0:μd≥0
HA:μd<0HA:μd<0(claim) - H0:μd≤0H0:μd≤0
HA:μd>0HA:μd>0(claim) - H0:μd=0H0:μd=0
HA:μd≠0HA:μd≠0(claim)
Given that αα is 0.01 the critical value is 2.584
The test statistic is: (round to 3 places)
The p-value is: (round to 3 places)
The decision can be made to:
- reject H0H0
- do not reject H0H0
The final conclusion is that:
- There is enough evidence to reject the claim that there was an increase in the scores.
- There is not enough evidence to reject the claim that there was an increase in the scores.
- There is enough evidence to support the claim that there was an increase in the scores.
- There is not enough evidence to support the claim that there was an increase in the scores.
Given data,
We have to test the claim that there was an increase in the scores.
Let,
Difference, d = Post-test – Pre-test
Hypothesis Formulation-
Null Hypothesis, H0: μD ≤ 0
Alternate Hypothesis, Ha: μD > 0
Since here population standard deviation is unknown so using t-test statistics.
Correct option is
H0:μd≤0
HA:μd>0(claim)
|
pre-test |
post-test |
d |
|
77 |
71 |
-6 |
|
48 |
53 |
5 |
|
68 |
61 |
-7 |
|
59 |
54 |
-5 |
|
75 |
76 |
1 |
|
65 |
73 |
8 |
|
50 |
57 |
7 |
|
100 |
106 |
6 |
|
55 |
61 |
6 |
|
98 |
91 |
-7 |
|
85 |
92 |
7 |
|
51 |
53 |
2 |
|
75 |
81 |
6 |
|
88 |
97 |
9 |
|
57 |
52 |
-5 |
|
70 |
77 |
7 |
|
55 |
64 |
9 |
|
|
Mean |
2.53 |
|
|
Sd.deviation |
6.05 |
Mean is 2.53
Standard deviation is 6.05
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