Question

A researcher wishes to test the effects of excerise on the ability to complete a basic skills test. He designs a pre-test and post-test to give to each participant. You believe that there was an increase in the scores. You believe the population of the differences is normally distributed, but you do not know the standard deviation. When calculating difference use Post-test minus Pre-test. pre-test post-test 52 60 60 55 44 49 92 94 84 76 55 65 64 58 67 66 53 59 99 99 75 79 77 82 Which of the following are the correct hypotheses? H 0 : μ d ≥ 0 H 0 : μ d ≥ 0 H A : μ d < 0 H A : μ d < 0 (claim) H 0 : μ d ≤ 0 H 0 : μ d ≤ 0 H A : μ d > 0 H A : μ d > 0 (claim) H 0 : μ d = 0 H 0 : μ d = 0 H A : μ d ≠ 0 H A : μ d ≠ 0 (claim) Correct

Given that α α is 0.10 the critical value is 1.363

The test statistic is: Incorrect(round to 3 places)

The p-value is: Incorrect(round to 3 places)

In an effort to improve the mathematical skills of 18 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
82	80
91	90
60	58
55	51
76	74
83	79
68	66
86	84
85	81
79	83
100	91
59	61
40	47
43	49
62	61
46	45
44	36
74	82

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 2.567
The test statistic is: (round to 3 places)
The p-value is: (round to 3 places)

Answer 1

In an effort to improve the mathematical skills of 18 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.

SOLUTION: H0:μd≤0
HA:μd>0 (claim)

(2) Rejection Region

Based on the information provided, the significance level is α=0.01, and the degrees of freedom are df=17.

Hence, it is found that the critical value for this right-tailed test is tc​=2.567, for α=0.01 and df=17.

The rejection region for this right-tailed test is R=t:t>2.567.

Test Statistics

The t-statistic is computed as shown in the following formula:

Decision about the null hypothesis

Since it is observed that t=−0.755≤tc​=2.567, it is then concluded that the null hypothesis is not rejected.

Using the P-value approach: The p-value is p=0.770, and since p=0.770≥0.01, it is concluded that the null hypothesis is not rejected.

(5) Conclusion

It is concluded that the null hypothesis Ho is not rejected. Therefore, there is not enough evidence to claim that the population mean μ1(POST TEST)​ is greater than μ2(PRE TEST)​, at the 0.01 significance level.

NOTE: PLEASE RE POST above question with data in tabular form.