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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 a difference 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. post-test 63 pre-test 71 97 94 66 66 41 32 96 97 41 45 79 81 98 106 76 70 63 70 42 47 86 94 Which of the following are the correct hypotheses? O Ho: Hd 2 0 HA: Ha < 0(claim) O Ho : µd <0 HA: Ha > 0(claim) O Ho: µa = 0 HA: Ha + 0(claim) Given that a is 0.05 the critical value is 2.201 and -2.201 The test statistic is: (round to 3 places) The p-value is: (round to 3 places) The decision can be made to: O reject Ho O do not reject Ho The final conclusion is that: O There is enough evidence to reject the claim that there was a difference in the scores. O There is not enough evidence to reject the claim that there was a difference in the scores. O There is enough evidence to support the claim that there was a difference in the scores. O There is not enough evidence to support the claim that there was a difference in the scores.

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 a difference 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. post-test 63 pre-test 71 97 94 66 66 41 32 96 97 41 45 79 81 98 106 76 70 63 70 42 47 86 94 Which of the following are the correct hypotheses? O Ho: Hd 2 0 HA: Ha < 0(claim) O Ho : µd <0 HA: Ha > 0(claim) O Ho: µa = 0 HA: Ha + 0(claim) Given that a is 0.05 the critical value is 2.201 and -2.201 The test statistic is: (round to 3 places) The p-value is: (round to 3 places) The decision can be made to: O reject Ho O do not reject Ho The final conclusion is that: O There is enough evidence to reject the claim that there was a difference in the scores. O There is not enough evidence to reject the claim that there was a difference in the scores. O There is enough evidence to support the claim that there was a difference in the scores. O There is not enough evidence to support the claim that there was a difference in the scores.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.4: Distributions Of Data
Problem 19PFA
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A researcher is investigating the effects of exercise on the ability to complete a basic skills test. To assess this, a pre-test and post-test are administered to participants. The researcher hypothesizes that there is a difference in scores due to exercise. The population differences are assumed to be normally distributed, but the standard deviation is unknown. For calculations, the difference is determined by subtracting the pre-test score from the post-test score. The table of scores is as follows: | pre-test | post-test | |----------|-----------| | 63 | 71 | | 97 | 94 | | 66 | 66 | | 41 | 32 | | 96 | 97 | | 41 | 45 | | 79 | 81 | | 98 | 106 | | 76 | 70 | | 63 | 70 | | 42 | 47 | | 86 | 94 | ### Hypothesis Testing **Which of the following are the correct hypotheses?** - \( H_0: \mu_d \geq 0 \) \( H_a: \mu_d < 0 \) (claim) - \( H_0: \mu_d \leq 0 \) \( H_a: \mu_d > 0 \) (claim) - \( H_0: \mu_d = 0 \) \( H_a: \mu_d \neq 0 \) (claim) Given that \( \alpha = 0.05 \), the critical value is 2.201 and -2.201. The test statistic is: \_\_\_\_\_\_\_\_\_ (round to 3 places) The p-value is: \_\_\_\_\_\_\_\_\_ (round to 3 places) The decision can be made to: - Reject \( H_0 \) - Do not reject \( H_0 \) **The final conclusion is that:** - There is enough evidence to reject the claim that there was a difference in the scores. - There is not enough evidence to reject the claim that there was a difference in the scores. - There is enough evidence to support the claim that there was a difference in the scores. - There is not enough evidence to support the claim that there was a
Transcribed Image Text:A researcher is investigating the effects of exercise on the ability to complete a basic skills test. To assess this, a pre-test and post-test are administered to participants. The researcher hypothesizes that there is a difference in scores due to exercise. The population differences are assumed to be normally distributed, but the standard deviation is unknown. For calculations, the difference is determined by subtracting the pre-test score from the post-test score. The table of scores is as follows: | pre-test | post-test | |----------|-----------| | 63 | 71 | | 97 | 94 | | 66 | 66 | | 41 | 32 | | 96 | 97 | | 41 | 45 | | 79 | 81 | | 98 | 106 | | 76 | 70 | | 63 | 70 | | 42 | 47 | | 86 | 94 | ### Hypothesis Testing **Which of the following are the correct hypotheses?** - \( H_0: \mu_d \geq 0 \) \( H_a: \mu_d < 0 \) (claim) - \( H_0: \mu_d \leq 0 \) \( H_a: \mu_d > 0 \) (claim) - \( H_0: \mu_d = 0 \) \( H_a: \mu_d \neq 0 \) (claim) Given that \( \alpha = 0.05 \), the critical value is 2.201 and -2.201. The test statistic is: \_\_\_\_\_\_\_\_\_ (round to 3 places) The p-value is: \_\_\_\_\_\_\_\_\_ (round to 3 places) The decision can be made to: - Reject \( H_0 \) - Do not reject \( H_0 \) **The final conclusion is that:** - There is enough evidence to reject the claim that there was a difference in the scores. - There is not enough evidence to reject the claim that there was a difference in the scores. - There is enough evidence to support the claim that there was a difference in the scores. - There is not enough evidence to support the claim that there was a
Expert Solution
Step 1

Given information-

Sample size, n = 12

Significance level, α = 0.05

We have given the critical value is 2.201 to -2.201.

Statistics homework question answer, step 1, image 1

We have to test the claim that there was a difference in score.

Hypothesis Formulation-

Null Hypothesis, H0: μD = 0

Alternate Hypothesis, Ha: μD ≠ 0 (Claim)

So, option C is correct.

Since here population standard deviation is unknown so using t-test statistics.

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