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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).     a. 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. H0​: μ1≥μ2 H1​: μ1<μ2   B. H0​: μ1=μ2 H1​: μ1≠μ2   C. H0​: μ1=μ2 H1​: μ1>μ2   D. H0​: μ1≠μ2 H1​: μ1<μ2   The test​ statistic, t, is: ______   The​ P-value is: ______   State the conclusion for the test.     A. Fail to reject the null hypothesis. There is 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. 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)?   ___ <μ1−μ2< ___ ​(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 ▼   zero, only positive values, only negative values,   so there ▼   is 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 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).     a. 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. H0​: μ1≥μ2 H1​: μ1<μ2   B. H0​: μ1=μ2 H1​: μ1≠μ2   C. H0​: μ1=μ2 H1​: μ1>μ2   D. H0​: μ1≠μ2 H1​: μ1<μ2   The test​ statistic, t, is: ______   The​ P-value is: ______   State the conclusion for the test.     A. Fail to reject the null hypothesis. There is 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. 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)?   ___ <μ1−μ2< ___ ​(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 ▼   zero, only positive values, only negative values,   so there ▼   is is not   sufficient evidence to support the claim that blue enhances performance on a creative task.

Holt Mcdougal Larson Pre-algebra: Student Edition 2012
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 1E
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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).
 
 
a. 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.
H0​:
μ1≥μ2
H1​:
μ1<μ2
 
B.
H0​:
μ1=μ2
H1​:
μ1≠μ2
 
C.
H0​:
μ1=μ2
H1​:
μ1>μ2
 
D.
H0​:
μ1≠μ2
H1​:
μ1<μ2
 
The test​ statistic, t, is: ______
 
The​ P-value is: ______
 
State the conclusion for the test.
 
 
A.
Fail to reject
the null hypothesis. There is 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.
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)?
 
___ <μ1−μ2< ___
​(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
▼
 
zero,
only positive values,
only negative values,
 
so there
▼
 
is
is not
 
sufficient evidence to support the claim that blue enhances performance on a creative task.
Response summary statistics Background X S Blue H1 35 3.67 0.53 Red H2 43 2.89 0.95
Transcribed Image Text:Response summary statistics Background X S Blue H1 35 3.67 0.53 Red H2 43 2.89 0.95
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