Words were displayed on a computer screen with background colors of red and blue. Results from scores
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
0.050.05
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?
| n | x overbarx | s | |
| Red Background | 3434 | 15.2915.29 | 5.925.92 |
| Blue Background | 3636 | 12.7512.75 | 5.415.41 |
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Part 1
What are the null and alternative hypotheses?
A.
Upper H 0H0:
sigma Subscript 1 Superscript 221equals=sigma Subscript 2 Superscript 222
Upper H 1H1:
sigma Subscript 1 Superscript 221greater than or equalssigma Subscript 2 Superscript 222
B.
Upper H 0H0:
sigma Subscript 1 Superscript 221equals=sigma Subscript 2 Superscript 222
Upper H 1H1:
sigma Subscript 1 Superscript 221less than C. Upper H 0H0: sigma Subscript 1 Superscript 221not equalssigma Subscript 2 Superscript 222 Upper H 1H1: sigma Subscript 1 Superscript 221equals=sigma Subscript 2 Superscript 222 D. Upper H 0H0: sigma Subscript 1 Superscript 221equals=sigma Subscript 2 Superscript 222 Upper H 1H1: sigma Subscript 1 Superscript 221not equalssigma Subscript 2 Superscript 222 Part 2 Identify the test statistic. Fequals=enter your response here (Round to two decimal places as needed.) Part 3 Use technology to identify the P-value. The P-value is enter your response here. (Round to three decimal places as needed.) Part 4 What is the conclusion for this hypothesis test? A. Fail to rejectFailtoreject Upper H 0H0. There is sufficientsufficient evidence to warrant rejection of the claim that the samples are from populations with the same standard deviation. B. RejectReject Upper H 0H0. There is insufficientinsufficient evidence to warrant rejection of the claim that the samples are from populations with the same standard deviation. C. Fail to rejectFailtoreject Upper H 0H0. There is insufficientinsufficient evidence to warrant rejection of the claim that the samples are from populations with the same standard deviation. D. RejectReject Upper H 0H0. There is sufficientsufficient evidence to warrant rejection of the claim that the samples are from populations with the same standard deviation. Part 5 Does the background color appear to have an effect on the variation of word recall scores? A. YesYes, the variation of word recall scores appears to be differentdifferent when the color is changed. B. YesYes, the variation of word recall scores appears to be the samethesame when the color is changed. C. NoNo, the variation of word recall scores appears to be the samethesame when the color is changed. D. NoNo, the variation of word recall scores appears to be differentdifferent when the color is changed.Expert Answer:
