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.

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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Related questions

Question

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?

H0:

μ1≥μ2

H1:

μ1<μ2

H0:

μ1=μ2

H1:

μ1≠μ2

H0:

μ1=μ2

H1:

μ1>μ2

H0:

μ1≠μ2

H1:

μ1<μ2

The test statistic, t, is: ______

The P-value is: ______

State the conclusion for the test.

Fail to reject

the null hypothesis. There is sufficient evidence to support the claim that blue enhances performance on a creative task.

Fail to reject

the null hypothesis. There is not sufficient evidence to support the claim that blue enhances performance on a creative task.

Reject

the null hypothesis. There is sufficient evidence to support the claim that blue enhances performance on a creative task.

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 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

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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