Question

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?

Answer 1

The null hypothesis (H0) is that there is no difference in performance between subjects with a blue background and subjects with a red background. The alternative hypothesis (Ha) is that blue enhances performance on a creative task.

Step-by-step explanation:

For this problem, we are testing the claim that blue enhances performance on a creative task. The null hypothesis (H0) is that there is no difference in performance between subjects with a blue background and subjects with a red background. The alternative hypothesis (Ha) is that blue enhances performance on a creative task.

To test this claim, we can use a two-sample t-test. We compare the mean creativity scores of the two groups and determine if the difference is statistically significant.

Answer 2

To test the claim that blue enhances creativity, we set a null hypothesis that there is no difference in creativity scores between red and blue backgrounds (μ1 = μ2) and an alternative hypothesis that blue backgrounds lead to higher creativity scores (μ2 > μ1). Using an independent two-sample t-test at a 0.01 significance level, we can determine if the evidence supports the claim.

Step-by-step explanation:

To test the claim that blue enhances performance on a creative task, we first need to define our null hypothesis (H0) and alternative hypothesis (Ha). The null hypothesis typically states that there is no effect or that the two groups do not differ, while the alternative hypothesis represents the claim we want to test - in this case, that the blue background leads to increased creativity.

Null Hypothesis (H0): The creativity scores for the red and blue backgrounds are the same, or more formally, μ1 = μ2, where μ1 is the mean creativity score with a red background and μ2 with a blue background.

Alternative Hypothesis (Ha): The creativity scores for a blue background are higher than those for a red background, or μ2 > μ1.

To test these hypotheses, we would perform a two-sample t-test for the difference of means, preferably an independent t-test since we're not assuming equal population standard deviations and the samples are independent. At the 0.01 significance level, if the p-value obtained is less than 0.01, we reject the null hypothesis, thereby supporting the claim that blue enhances performance on a creative task.