To compare two elementary schools regarding teaching of reading skills, 12 sets of identical twins were used. In each case, one child was selected at random and sent to school A, and his or her twin was sent to school B. Near the end of fifth grade, an achievement test was given to each child. The results follow. Twin Pair 1 2 3 4 5 6 School A 179 154 112 99 120 115 School B 82 131 117 118 114 84 Twin Pair 7 8 9 10 11 12 School A 88 119 112 148 129 87 School B 95 75 92 136 147 101 Use a 0.05 level of significance to test the hypothesis that the two schools have the same effectiveness in teaching reading skills against the alternate hypothesis that the schools are not equally effective. (a) What is the level of significance? State the null and alternate hypotheses. Ho: Distributions are the same. H1: Distributions are different.Ho: Distributions are the same. H1: Distributions are the same. Ho: Distributions are different. H1: Distributions are the same.Ho: Distributions are different. H1: Distributions are different. (b) Compute the sample test statistic. (Round your answer to two decimal places.) What sampling distribution will you use? normalStudent's t uniformchi-square (c) Find the P-value of the sample test statistic. (Round your answer to four decimal places.) (d) What can you conclude about the test? At the ? = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.At the ? = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant. At the ? = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.At the ? = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant. (e) Interpret your conclusion in the context of the application. Reject the null hypothesis, there is sufficient evidence that the schools are not equally effective.Fail to reject the null hypothesis, there is sufficient evidence that the schools are not equally effective. Fail to reject the null hypothesis, there is insufficient evidence that the schools are not equally effective.Reject the null hypothesis, there is insufficient evidence that the schools are not equally effective.

To compare two elementary schools regarding teaching of reading skills, 12 sets of identical twins were used. In each case, one child was selected at random and sent to school A, and his or her twin was sent to school B. Near the end of fifth grade, an achievement test was given to each child. The results follow. Twin Pair 1 2 3 4 5 6 School A 179 154 112 99 120 115 School B 82 131 117 118 114 84 Twin Pair 7 8 9 10 11 12 School A 88 119 112 148 129 87 School B 95 75 92 136 147 101 Use a 0.05 level of significance to test the hypothesis that the two schools have the same effectiveness in teaching reading skills against the alternate hypothesis that the schools are not equally effective. (a) What is the level of significance? State the null and alternate hypotheses. Ho: Distributions are the same. H1: Distributions are different.Ho: Distributions are the same. H1: Distributions are the same. Ho: Distributions are different. H1: Distributions are the same.Ho: Distributions are different. H1: Distributions are different. (b) Compute the sample test statistic. (Round your answer to two decimal places.) What sampling distribution will you use? normalStudent's t uniformchi-square (c) Find the P-value of the sample test statistic. (Round your answer to four decimal places.) (d) What can you conclude about the test? At the ? = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.At the ? = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant. At the ? = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.At the ? = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant. (e) Interpret your conclusion in the context of the application. Reject the null hypothesis, there is sufficient evidence that the schools are not equally effective.Fail to reject the null hypothesis, there is sufficient evidence that the schools are not equally effective. Fail to reject the null hypothesis, there is insufficient evidence that the schools are not equally effective.Reject the null hypothesis, there is insufficient evidence that the schools are not equally effective.

Holt Mcdougal Larson Pre-algebra: Student Edition 2012

1st Edition

ISBN:9780547587776

Author:HOLT MCDOUGAL

Publisher:HOLT MCDOUGAL

Chapter11: Data Analysis And Probability

Section11.5: Interpreting Data

Problem 1C

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Question

Twin Pair	1	2	3	4	5	6
School A	179	154	112	99	120	115
School B	82	131	117	118	114	84

Twin Pair	7	8	9	10	11	12
School A	88	119	112	148	129	87
School B	95	75	92	136	147	101

Use a 0.05 level of significance to test the hypothesis that the two schools have the same effectiveness in teaching reading skills against the alternate hypothesis that the schools are not equally effective.

(a) What is the level of significance?

State the null and alternate hypotheses.

H_o: Distributions are the same. H₁: Distributions are different.H_o: Distributions are the same. H₁: Distributions are the same. H_o: Distributions are different. H₁: Distributions are the same.H_o: Distributions are different. H₁: Distributions are different.

(b) Compute the sample test statistic. (Round your answer to two decimal places.)

What sampling distribution will you use?

normalStudent's t uniformchi-square

(c) Find the P-value of the sample test statistic. (Round your answer to four decimal places.)

(d) What can you conclude about the test?

At the ? = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.At the ? = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant. At the ? = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.At the ? = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.

(e) Interpret your conclusion in the context of the application.

Reject the null hypothesis, there is sufficient evidence that the schools are not equally effective.Fail to reject the null hypothesis, there is sufficient evidence that the schools are not equally effective. Fail to reject the null hypothesis, there is insufficient evidence that the schools are not equally effective.Reject the null hypothesis, there is insufficient evidence that the schools are not equally effective.

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