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Ch. 9 - Inferences from Two Samples
Triola - Elementary Statistics 14th Edition
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Tutti i libri di testoTriola 14th EditionCh. 9 - Inferences from Two SamplesProblema 9.2.10a
Capitolo 9, Problema 9.2.10a

In Exercises 5–20, 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. (Note: Answers in Appendix D include technology answers based on Formula 9-1 along with “Table” answers based on Table A-3 with df equal to the smaller of n1-1 and n2-1)


Color and Creativity Researchers from the University of British Columbia 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 below. Higher scores correspond to more creativity. The researchers make the claim that “blue enhances performance on a creative task.”


a. Use a 0.01 significance level to test the claim that blue enhances performance on a creative task.


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Step 1: Define the null hypothesis (H₀) and the alternative hypothesis (H₁). H₀: There is no difference in creativity scores between the red and blue backgrounds (μ₁ = μ₂). H₁: Blue enhances performance on a creative task, meaning the mean creativity score for the blue background is greater than the mean score for the red background (μ₂ > μ₁).
Step 2: Identify the significance level (α). The problem specifies a significance level of 0.01, which will be used to determine whether to reject the null hypothesis.
Step 3: Calculate the test statistic using the formula for a two-sample t-test for independent samples: t = (x̄₁ - x̄₂) / √((s₁²/n₁) + (s₂²/n₂)). Here, x̄₁ = 3.39, s₁ = 0.97, n₁ = 35 for the red background, and x̄₂ = 3.97, s₂ = 0.63, n₂ = 36 for the blue background.
Step 4: Determine the degrees of freedom (df) using the formula: df = min(n₁ - 1, n₂ - 1). In this case, df = min(35 - 1, 36 - 1) = 34. Use this df to find the critical t-value from a t-distribution table or technology for a one-tailed test at α = 0.01.
Step 5: Compare the calculated t-value to the critical t-value. If the calculated t-value exceeds the critical t-value, reject the null hypothesis (H₀) and conclude that blue enhances performance on a creative task. Otherwise, fail to reject H₀.

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Hypothesis Testing

Hypothesis testing is a statistical method used to make decisions about a population based on sample data. It involves formulating a null hypothesis (H0) and an alternative hypothesis (H1), then using sample statistics to determine whether to reject H0 in favor of H1. In this case, the null hypothesis would state that there is no difference in creativity scores between the red and blue backgrounds, while the alternative would claim that the blue background enhances creativity.
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Step 1: Write Hypotheses

Significance Level

The significance level, denoted as alpha (α), is the threshold for determining whether a result is statistically significant. In this scenario, a significance level of 0.01 indicates that there is a 1% risk of concluding that a difference exists when there is none. This level is used to assess the strength of the evidence against the null hypothesis, with lower values indicating a stricter criterion for significance.
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Step 4: State Conclusion Example 4

Independent Samples t-Test

An independent samples t-test is a statistical test used to compare the means of two independent groups to determine if there is a significant difference between them. In this case, the test will compare the creativity scores of subjects with red and blue backgrounds. The test accounts for sample sizes, means, and standard deviations to calculate a t-statistic, which is then compared to a critical value based on the chosen significance level.
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Sampling Distribution of Sample Proportion
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