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Researchers conducted trials to investigate the effects of color on creativity. Subjects with a red background were asked to think of creative uses for a brick; other subjects with a blue background were given the same task. Responses were scored by a panel of judges and results from scores of creativity are given in the accompanying table. Higher scores correspond to more creativity. The researchers make the claim that "blue enhances performance on a creative task." Assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. Complete parts (a) and (b). Click the icon to view the summary statistics. a. Use a 0.01 significance level to test the claim that blue enhances performance on a creative task. What are the null and alternative hypotheses? OA. H: ₁2₂ H₁: ₁ P₂ OD. H₂: #₁ #₂ H₁: #₁ #₂ b. Construct the confidence interval suitable for testing the claim in part (a). What is it about the confidence interval that results in the same conclusion from part (a)?

Researchers conducted trials to investigate the effects of color on creativity. Subjects with a red background were asked to think of creative uses for a brick; other subjects with a blue background were given the same task. Responses were scored by a panel of judges and results from scores of creativity are given in the accompanying table. Higher scores correspond to more creativity. The researchers make the claim that "blue enhances performance on a creative task." Assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. Complete parts (a) and (b). Click the icon to view the summary statistics. a. Use a 0.01 significance level to test the claim that blue enhances performance on a creative task. What are the null and alternative hypotheses? OA. H: ₁2₂ H₁: ₁ P₂ OD. H₂: #₁ #₂ H₁: #₁ #₂ b. Construct the confidence interval suitable for testing the claim in part (a). What is it about the confidence interval that results in the same conclusion from part (a)?

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
Section10.6: Summarizing Categorical Data
Problem 10CYU
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Researchers conducted trials to investigate the effects of color on creativity. Subjects with a red background were asked to think of creative uses for a brick; other subjects with a blue background were given the same task. Responses were scored by a panel of judges and results from scores of creativity are given in the accompanying table. Higher scores correspond to more creativity. The researchers make the claim that "blue enhances performance on a creative task." Assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. Complete parts (a) and (b). Click the icon to view the summary statistics. a. Use a 0.01 significance level to test the claim that blue enhances performance on a creative task. What are the null and alternative hypotheses? OA. Ho: H₁ H₂ H₁: H₁ H₂ OC. Ho: H₁ H₂ H₁: H₁ H₂ The test statistic, t, is (Round to two decimal places as needed.) The P-value is (Round to three decimal places as needed.) State the conclusion for the test. C OB. Ho: H₁ H₂ H₁: H₁ H₂ OD. Ho: HH2 H₁: H₁ H₂ O A. Reject the null hypothesis. There is sufficient evidence to support the claim that blue enhances performance on a creative task. OB. Reject the null hypothesis. There is not sufficient evidence to support the claim that blue enhances performance on a creative task. O C. Fail to reject the null hypothesis. There is sufficient evidence to support the claim that blue enhances performance on a creative task. O D. Fail to reject the null hypothesis. There is not sufficient evidence to support the claim that blue enhances performance on a creative task. b. Construct the confidence interval suitable for testing the claim in part (a). What is it about the confidence interval that results in the same conclusion from part (a)? <H4-H₂ <[ (Round to two decimal places as needed.) What is it about the confidence interval that results in the same conclusion from part (a)? The confidence interval contains so there ▼sufficient evidence to support the claim that blue enhances performance on a creative task. Response Summary Statistics Background µ n Blue Red Print X H₁ 44 3.85 H₂ S 0.67 39 2.87 0.96 Done X
Transcribed Image Text:Researchers conducted trials to investigate the effects of color on creativity. Subjects with a red background were asked to think of creative uses for a brick; other subjects with a blue background were given the same task. Responses were scored by a panel of judges and results from scores of creativity are given in the accompanying table. Higher scores correspond to more creativity. The researchers make the claim that "blue enhances performance on a creative task." Assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. Complete parts (a) and (b). Click the icon to view the summary statistics. a. Use a 0.01 significance level to test the claim that blue enhances performance on a creative task. What are the null and alternative hypotheses? OA. Ho: H₁ H₂ H₁: H₁ H₂ OC. Ho: H₁ H₂ H₁: H₁ H₂ The test statistic, t, is (Round to two decimal places as needed.) The P-value is (Round to three decimal places as needed.) State the conclusion for the test. C OB. Ho: H₁ H₂ H₁: H₁ H₂ OD. Ho: HH2 H₁: H₁ H₂ O A. Reject the null hypothesis. There is sufficient evidence to support the claim that blue enhances performance on a creative task. OB. Reject the null hypothesis. There is not sufficient evidence to support the claim that blue enhances performance on a creative task. O C. Fail to reject the null hypothesis. There is sufficient evidence to support the claim that blue enhances performance on a creative task. O D. Fail to reject the null hypothesis. There is not sufficient evidence to support the claim that blue enhances performance on a creative task. b. Construct the confidence interval suitable for testing the claim in part (a). What is it about the confidence interval that results in the same conclusion from part (a)? <H4-H₂ <[ (Round to two decimal places as needed.) What is it about the confidence interval that results in the same conclusion from part (a)? The confidence interval contains so there ▼sufficient evidence to support the claim that blue enhances performance on a creative task. Response Summary Statistics Background µ n Blue Red Print X H₁ 44 3.85 H₂ S 0.67 39 2.87 0.96 Done X
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