9.10 Words were displayed on a computer screen with background colors of red and blue. Results from scores on a test of word recall are given below. Use a 0.05 significance level to test the claim that the samples are from populations with the same standard deviation. Assume that both samples are independent simple random samples from populations having normal distributions. Does the background color appear to have an effect on the variation of word recall scores?| Background | n | $ \bar{x} $ | s ||------------------|----|---------------|-----|| Red Background | 34 | 15.55 | 5.96|| Blue Background | 36 | 12.41 | 5.49|In this context:- $ n $ represents the sample size.- $ \bar{x} $ is the sample mean.- $ s $ is the sample standard deviation. ### Hypothesis Testing ExerciseThis exercise focuses on determining the null and alternative hypotheses, calculating the test statistic, finding the P-value, and drawing a conclusion from a hypothesis test. It explores whether color has an effect on the variation of word recall scores.#### Step 1: Formulating HypothesesIdentify the null and alternative hypotheses from the options provided:- **Option A:** - Null Hypothesis (H₀): σ₁² = σ₂² - Alternative Hypothesis (H₁): σ₁² < σ₂²- **Option B:** - Null Hypothesis (H₀): σ₁² = σ₂² - Alternative Hypothesis (H₁): σ₁² ≠ σ₂²- **Option C:** - Null Hypothesis (H₀): σ₁² = σ₂² - Alternative Hypothesis (H₁): σ₁² > σ₂²- **Option D:** - Null Hypothesis (H₀): σ₁² ≠ σ₂² - Alternative Hypothesis (H₁): σ₁² = σ₂²#### Step 2: Calculating the Test Statistic- Calculate and round off the test statistic to two decimal places, as needed.#### Step 3: Determining the P-Value- Use technology to determine the P-value and round it to three decimal places.#### Step 4: Conclusion from the Hypothesis TestChoose the conclusion based on the P-value:- **Option A:** Reject H₀. There is insufficient evidence to warrant rejection of the claim that the samples are from populations with the same standard deviation.- **Option B:** Fail to reject H₀. There is sufficient evidence to warrant rejection of the claim that the samples are from populations with the same standard deviation.- **Option C:** Fail to reject H₀. There is insufficient evidence to warrant rejection of the claim that the samples are from populations with the same standard deviation.- **Option D:** Fail to reject H₀. There is sufficient evidence to warrant rejection of the claim that the samples are from populations with the same standard deviation.#### Analysis of the Effect of Color on Word Recall ScoresReflect on how the background color impacts word recall score variation:- **Option A:** Yes, the variation of word recall scores appears to

Answered: Image /qna-images/answer/ad4b290a-8fda-46b3-b49f-e0ed0a660816.jpg

Words were displayed on a computer screen with background colors of red and blue. Results from scores on a test of wor recall are given below. Use a 0.05 significance level to test the claim that the samples are from populations with the same standard deviation. Assume that both samples are independent simple random samples from populations having normal distributions. Does the background color appear to have an effect on the variation of word recall scores? Red Background Blue Background n 34 15.55 36 12.41 S 5.96 5.49

Words were displayed on a computer screen with background colors of red and blue. Results from scores on a test of wor recall are given below. Use a 0.05 significance level to test the claim that the samples are from populations with the same standard deviation. Assume that both samples are independent simple random samples from populations having normal distributions. Does the background color appear to have an effect on the variation of word recall scores? Red Background Blue Background n 34 15.55 36 12.41 S 5.96 5.49

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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Question

9.10

Words were displayed on a computer screen with background colors of red and blue. Results from scores on a test of word recall are given below. Use a 0.05 significance level to test the claim that the samples are from populations with the same standard deviation. Assume that both samples are independent simple random samples from populations having normal distributions. Does the background color appear to have an effect on the variation of word recall scores?

| Background | n | $ \bar{x} $ | s |
|------------------|----|---------------|-----|
| Red Background | 34 | 15.55 | 5.96|
| Blue Background | 36 | 12.41 | 5.49|

In this context:
- $ n $ represents the sample size.
- $ \bar{x} $ is the sample mean.
- $ s $ is the sample standard deviation.

### Hypothesis Testing Exercise

This exercise focuses on determining the null and alternative hypotheses, calculating the test statistic, finding the P-value, and drawing a conclusion from a hypothesis test. It explores whether color has an effect on the variation of word recall scores.

#### Step 1: Formulating Hypotheses

Identify the null and alternative hypotheses from the options provided:

- **Option A:**
- Null Hypothesis (H₀): σ₁² = σ₂²
- Alternative Hypothesis (H₁): σ₁² < σ₂²

- **Option B:**
- Null Hypothesis (H₀): σ₁² = σ₂²
- Alternative Hypothesis (H₁): σ₁² ≠ σ₂²

- **Option C:**
- Null Hypothesis (H₀): σ₁² = σ₂²
- Alternative Hypothesis (H₁): σ₁² > σ₂²

- **Option D:**
- Null Hypothesis (H₀): σ₁² ≠ σ₂²
- Alternative Hypothesis (H₁): σ₁² = σ₂²

#### Step 2: Calculating the Test Statistic

- Calculate and round off the test statistic to two decimal places, as needed.

#### Step 3: Determining the P-Value

- Use technology to determine the P-value and round it to three decimal places.

#### Step 4: Conclusion from the Hypothesis Test

Choose the conclusion based on the P-value:

- **Option A:** Reject H₀. There is insufficient evidence to warrant rejection of the claim that the samples are from populations with the same standard deviation.
- **Option B:** Fail to reject H₀. There is sufficient evidence to warrant rejection of the claim that the samples are from populations with the same standard deviation.
- **Option C:** Fail to reject H₀. There is insufficient evidence to warrant rejection of the claim that the samples are from populations with the same standard deviation.
- **Option D:** Fail to reject H₀. There is sufficient evidence to warrant rejection of the claim that the samples are from populations with the same standard deviation.

#### Analysis of the Effect of Color on Word Recall Scores

Reflect on how the background color impacts word recall score variation:

- **Option A:** Yes, the variation of word recall scores appears to

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