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).
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The test statistic, $t$, is 4.96 . (Round to two decimal places as needed.)
The P-value is 0.000 . (Round to three decimal places as needed.)
State the conclusion for the test.
A. 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 not 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.
Answer
Final Answer: \boxed{\text{A. Reject the null hypothesis. There is sufficient evidence to support the claim that blue enhances performance on a creative task.}}
Step 1 ：The test statistic, t, is 4.96 and the P-value is 0.000. In hypothesis testing, a P-value less than 0.05 is typically considered statistically significant, meaning we would reject the null hypothesis. The null hypothesis in this case would be that there is no difference in creativity between the red and blue backgrounds. Since the P-value is less than 0.05, we reject the null hypothesis. Therefore, there is sufficient evidence to support the claim that blue enhances performance on a creative task.
Step 2 ：Final Answer: \boxed{\text{A. Reject the null hypothesis. There is sufficient evidence to support the claim that blue enhances performance on a creative task.}}
