Question

In: Math

You wish to test the following claim ( H a ) at a significance level of...

You wish to test the following claim ( H a ) at a significance level of α = 0.10 . For the context of this problem, μ d = μ 2 − μ 1 where the first data set represents a pre-test and the second data set represents a post-test. H o : μ d = 0 H a : μ d < 0 You believe the population of difference scores is normally distributed, but you do not know the standard deviation. You obtain pre-test and post-test samples for n = 15 subjects. The average difference (post - pre) is ¯ d = − 15.1 with a standard deviation of the differences of s d = 41.8 . What is the test statistic for this sample? (Report answer accurate to three decimal places.) test statistic = What is the p-value for this sample? (Report answer accurate to four decimal places.) p-value = The p-value is... less than (or equal to) α greater than α This test statistic leads to a decision to... reject the null accept the null fail to reject the null As such, the final conclusion is that... There is sufficient evidence to warrant rejection of the claim that the mean difference of post-test from pre-test is less than 0. There is not sufficient evidence to warrant rejection of the claim that the mean difference of post-test from pre-test is less than 0. The sample data support the claim that the mean difference of post-test from pre-test is less than 0. There is not sufficient sample evidence to support the claim that the mean difference of post-test from pre-test is less than 0

Solutions

Expert Solution

hypothesis:-

given data are:-

-15.1

standard deviation of differences () = 41.8

sample size (n) = 15

level of significance () = 0.10

so, our test statistic be:-

degrees of freedom= (n-1) = (15-1) = 14

p value = 0.0918 (using p value calculator, for t score = -1.399, df=14 , one sided test)

decision:-

p value = 0.0918 < 0.10 ( level of significance)

so, p value <

This test statistic leads to a decision to reject the null hypothesis.

As such, the final conclusion is that:-

There is not sufficient sample evidence to support the claim that the mean difference of post-test from pre-test is less than 0

***If you have any doubt regarding the problem please write it in the comment section.if you are satisfied please give me a LIKE if possible...


Related Solutions

You wish to test the following claim ( H a ) at a significance level of...
You wish to test the following claim ( H a ) at a significance level of α = 0.002 . H o : μ = 73.8 H a : μ > 73.8 You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n = 31 with mean M = 83.5 and a standard deviation of S D = 16.9 . What is the test statistic for this sample? (Report...
You wish to test the following claim ( H a ) at a significance level of...
You wish to test the following claim ( H a ) at a significance level of α = 0.01 . H o : μ 1 = μ 2 H a : μ 1 < μ 2 You believe both populations are normally distributed, but you do not know the standard deviations for either. However, you also have no reason to believe the variances of the two populations are not equal. You obtain a sample of size n 1 = 24...
You wish to test the following claim ( H a ) at a significance level of...
You wish to test the following claim ( H a ) at a significance level of α = 0.02 . H o : p 1 = p 2 H a : p 1 < p 2 You obtain 159 successes in a sample of size n 1 = 646 from the first population. You obtain 66 successes in a sample of size n 2 = 221 from the second population. What is the test statistic for this sample? (Report answer...
You wish to test the following claim ( H a ) at a significance level of...
You wish to test the following claim ( H a ) at a significance level of α = 0.002 . H o : μ 1 = μ 2 H a : μ 1 ≠ μ 2 You believe both populations are normally distributed, but you do not know the standard deviations for either. However, you also have no reason to believe the variances of the two populations are not equal. You obtain the following two samples of data. Sample #1...
You wish to test the following claim ( H a ) at a significance level of...
You wish to test the following claim ( H a ) at a significance level of α = 0.005 . H o : μ = 50.7 H a : μ ≠ 50.7 You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n = 5 with mean M = 26.7 and a standard deviation of S D = 14.5 . What is the p-value for this sample? (Report answer...
You wish to test the following claim ( H a ) at a significance level of...
You wish to test the following claim ( H a ) at a significance level of α = 0.02 . H o : p 1 = p 2 H a : p 1 < p 2 You obtain 205 successes in a sample of size n 1 = 228 from the first population. You obtain 324 successes in a sample of size n 2 = 320 from the second population. For this test, you should NOT use the continuity correction,...
You wish to test the following claim ( H a ) at a significance level of...
You wish to test the following claim ( H a ) at a significance level of α = 0.005 . For the context of this problem, μ d = P o s t T e s t − P r e T e s t one data set represents a pre-test and the other data set represents a post-test. Each row represents the pre and post test scores for an individual. H o : μ d = 0 H a...
You wish to test the following claim ( H a ) at a significance level of...
You wish to test the following claim ( H a ) at a significance level of α = 0.005 . H o : p 1 = p 2 H a : p 1 > p 2 You obtain a sample from the first population with 210 successes and 90 failures. You obtain a sample from the second population with 152 successes and 124 failures. What is the critical value for this test? (Report answer accurate to three decimal places.) critical...
You wish to test the following claim ( H a ) at a significance level of...
You wish to test the following claim ( H a ) at a significance level of α = 0.05 . H o : μ = 73.7 H a : μ < 73.7 You believe the population is normally distributed, but you do not know the standard deviation. Your sample has: size: n = 107 mean: M = 69.7 standard deviation: S D = 10.2 . What is the test statistic for this sample? (Round the answer accurate to 3 decimal...
You wish to test the following claim ( H a ) at a significance level of...
You wish to test the following claim ( H a ) at a significance level of α = 0.005 H o : p 1 = p 2 H a : p 1 < p 2 You obtain 91.1% successes in a sample of size n 1 = 651 from the first population. You obtain 94.8% successes in a sample of size n 2 = 621 from the second population. For this test, you should NOT use the continuity correction, and...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT