Words were displayed on a computer screen with background colors of red and blue

Question

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? 35 15.16 5.99 Red Background Blue Background 36 12.12 5.48 What are the null and altenative hypotheses? o 2zo2 0 262 112 ldentify the test statistic. F = | (Round to two decimal places as needed.) Use technology to identify the P-value. The P-value is (Round to three decimal places as needed.) What is the conclusion for this hypothesis test? 0 A. Reject Ho There is insufficient evidence to warrant rejection of the claim that the samples are from populations with the same standard deviation. O B. Reject Ho. There is sufficient evidence to warrant rejection of the claim that the samples are from populations with the same standard deviation ° C. Fail to reject Ho. There is insufficient evidence to warrant rejection of the claim that the samples are from populations with the same standard deviation. 0 D. Fail to reject Ho. There is sufficient evidence to warrant rejection of the aim that the samples are from populations with the same standard deviation. Does the background color appear to have an effect on the variation of word recall scores? 0 A. No, the variation of word recall scores appears to be different when the color is changed. O B. No, the variation of word recall scores appears to be the same when the color is changed. ° C. Yes, the variation of word recall scores appears to be different when the color is changed. 0 D. Yes, the variation of word recall scores appears to be the same when the color is changed.

Explanation / Answer

The statistical software output for this problem is:

Two sample variance summary hypothesis test:
12 : Variance of population 1
22 : Variance of population 2
12/22 : Ratio of two variances
H0 : 12/22 = 1
HA : 12/22 1

Hypothesis test results:

Hence,

Hypotheses:

H0 : 12 = 22
HA : 12 22

Option C is correct.

F = 1.19

P - value = 0.603

Conclusion: Option C is correct.

Does the background color appear to have an effect? Option B is correct.

Ratio Num. DF Den. DF Sample Ratio F-Stat P-value 12/22 34 35 1.1947926 1.1947926 0.6028

Related Questions

Navigate

• Browse (All)
• Browse W
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.