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Use 0.05 significance level to test the daim that blue enhances performance on a creative task. What are the null and alternative hypotheses? CAH₂₂₂ H₂ 14 51₂ OCH ₂ 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 tast ⒸA. Reject the null hypothesis. There is not sufficient evidence to support the claim that blue anhances performance on a creative task CB. Fail to reject the null hypothesis. There is not sufficient evidence to support the claim that blue enhances performance on a creative task. OC. Reject the null hypothesis. There is sufficient evidence to support the claim that blue enhances performance on a creative task CD. Feil to reject the null hypothesis. There is sufficient evidence to support the daim that blue entences performance on a creative task. OBH₂=₂ GD hư không có không H₂ 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)? <4-1₂ (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 containe so there sufficient evidence to support the claim that blue enhances performance on a creative lask

Use 0.05 significance level to test the daim that blue enhances performance on a creative task. What are the null and alternative hypotheses? CAH₂₂₂ H₂ 14 51₂ OCH ₂ 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 tast ⒸA. Reject the null hypothesis. There is not sufficient evidence to support the claim that blue anhances performance on a creative task CB. Fail to reject the null hypothesis. There is not sufficient evidence to support the claim that blue enhances performance on a creative task. OC. Reject the null hypothesis. There is sufficient evidence to support the claim that blue enhances performance on a creative task CD. Feil to reject the null hypothesis. There is sufficient evidence to support the daim that blue entences performance on a creative task. OBH₂=₂ GD hư không có không H₂ 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)? <4-1₂ (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 containe so there sufficient evidence to support the claim that blue enhances performance on a creative lask

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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**Hypothesis Testing on Creativity Enhancement Using Blue** **8. Use a 0.05 significance level to test the claim that blue enhances performance on a creative task.** **What are the null and alternative hypotheses?** - **A.** \( H_0: \mu_1 \neq \mu_2 \) \( H_1: \mu_1 = \mu_2 \) - **B.** \( H_0: \mu_1 = \mu_2 \) \( H_1: \mu_1 \neq \mu_2 \) - **C.** \( H_0: \mu_1 \le \mu_2 \) \( H_1: \mu_1 > \mu_2 \) - **D.** \( H_0: \mu_1 \ge \mu_2 \) \( H_1: \mu_1 < \mu_2 \) **The test statistic is:** \( t = \boxed{\ } \) (Round to two decimal places as needed.) **The P-value is:** \( \boxed{\ } \) (Round to three decimal places as needed.) **State the conclusion for the test:** - **A.** Reject the null hypothesis. There is not sufficient evidence to support the claim that blue enhances performance on a creative task. - **B.** Fail to reject the null hypothesis. There is not sufficient evidence to support the claim that blue enhances performance on a creative task. - **C.** Reject the null hypothesis. There is sufficient evidence to support the claim that blue enhances performance on a creative task. - **D.** Fail to reject the null hypothesis. There is 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)?** \(- \infty < \mu_1 - \mu_2 < \boxed{\ }\) (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 \(\boxed{\ } \) so there \(\boxed{\text{is not}}\) sufficient evidence to support the claim that blue enhances performance on a creative task.
Transcribed Image Text:**Hypothesis Testing on Creativity Enhancement Using Blue** **8. Use a 0.05 significance level to test the claim that blue enhances performance on a creative task.** **What are the null and alternative hypotheses?** - **A.** \( H_0: \mu_1 \neq \mu_2 \) \( H_1: \mu_1 = \mu_2 \) - **B.** \( H_0: \mu_1 = \mu_2 \) \( H_1: \mu_1 \neq \mu_2 \) - **C.** \( H_0: \mu_1 \le \mu_2 \) \( H_1: \mu_1 > \mu_2 \) - **D.** \( H_0: \mu_1 \ge \mu_2 \) \( H_1: \mu_1 < \mu_2 \) **The test statistic is:** \( t = \boxed{\ } \) (Round to two decimal places as needed.) **The P-value is:** \( \boxed{\ } \) (Round to three decimal places as needed.) **State the conclusion for the test:** - **A.** Reject the null hypothesis. There is not sufficient evidence to support the claim that blue enhances performance on a creative task. - **B.** Fail to reject the null hypothesis. There is not sufficient evidence to support the claim that blue enhances performance on a creative task. - **C.** Reject the null hypothesis. There is sufficient evidence to support the claim that blue enhances performance on a creative task. - **D.** Fail to reject the null hypothesis. There is 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)?** \(- \infty < \mu_1 - \mu_2 < \boxed{\ }\) (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 \(\boxed{\ } \) so there \(\boxed{\text{is not}}\) sufficient evidence to support the claim that blue enhances performance on a creative task.
Researchers conducted trials to investigate the effects of color on creativity. Subjects with a red background were tasked with thinking of creative uses for a brick, while those with a blue background were given the same task. Responses were scored by a panel of judges, and the results are summarized in the accompanying table. Higher scores correspond to more creativity. Researchers claim that "blue enhances performance on a creative task." It is assumed that the two samples are independent simple random samples selected from normally distributed populations, without assuming the population standard deviations are equal. **Task:** Use a 0.05 significance level to test the claim that blue enhances performance on a creative task. **Null and Alternative Hypotheses:** - A. \( H_0: \mu_1 \neq \mu_2 \) and \( H_1: \mu_1 < \mu_2 \) - B. \( H_0: \mu_1 = \mu_2 \) and \( H_1: \mu_1 > \mu_2 \) - C. \( H_0: \mu_1 \geq \mu_2 \) and \( H_1: \mu_1 < \mu_2 \) - D. \( H_0: \mu_1 = \mu_2 \) and \( H_1: \mu_1 \neq \mu_2 \) **Response Summary Statistics:** - **Backgrounds:** - **Blue** (\(\mu_1\)): - Sample size (\(n\)): 47 - Mean score (\(\bar{x}\)): 4.03 - Standard deviation (\(s\)): 0.66 - **Red** (\(\mu_2\)): - Sample size (\(n\)): 45 - Mean score (\(\bar{x}\)): 3.49 - Standard deviation (\(s\)): 0.84 The table below summarizes these statistics. | Background | \( n \) | \( \bar{x} \) | \( s \) | |------------|--------|--------|-------| | Blue | 47 | 4.03 | 0.66 | | Red | 45 | 3.49 | 0.84 |
Transcribed Image Text:Researchers conducted trials to investigate the effects of color on creativity. Subjects with a red background were tasked with thinking of creative uses for a brick, while those with a blue background were given the same task. Responses were scored by a panel of judges, and the results are summarized in the accompanying table. Higher scores correspond to more creativity. Researchers claim that "blue enhances performance on a creative task." It is assumed that the two samples are independent simple random samples selected from normally distributed populations, without assuming the population standard deviations are equal. **Task:** Use a 0.05 significance level to test the claim that blue enhances performance on a creative task. **Null and Alternative Hypotheses:** - A. \( H_0: \mu_1 \neq \mu_2 \) and \( H_1: \mu_1 < \mu_2 \) - B. \( H_0: \mu_1 = \mu_2 \) and \( H_1: \mu_1 > \mu_2 \) - C. \( H_0: \mu_1 \geq \mu_2 \) and \( H_1: \mu_1 < \mu_2 \) - D. \( H_0: \mu_1 = \mu_2 \) and \( H_1: \mu_1 \neq \mu_2 \) **Response Summary Statistics:** - **Backgrounds:** - **Blue** (\(\mu_1\)): - Sample size (\(n\)): 47 - Mean score (\(\bar{x}\)): 4.03 - Standard deviation (\(s\)): 0.66 - **Red** (\(\mu_2\)): - Sample size (\(n\)): 45 - Mean score (\(\bar{x}\)): 3.49 - Standard deviation (\(s\)): 0.84 The table below summarizes these statistics. | Background | \( n \) | \( \bar{x} \) | \( s \) | |------------|--------|--------|-------| | Blue | 47 | 4.03 | 0.66 | | Red | 45 | 3.49 | 0.84 |
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