A study was done using a treatment group and a placebo group. The results are shown in the table. 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) below. Use a 0.10 significance level for both parts. a. Test the claim that the two samples are from populations with the same mean. What are the null and alternative hypotheses? OA. Ho: H₁ H₂ H₁:₁ H₂ OB. Ho: ₁₂ H₁: H₁ H₂ OD. Ho: H₁

College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
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Chapter8: Sequences, Series, And Probability
Section8.7: Probability
Problem 58E: What is meant by the sample space of an experiment?
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A study was done using a treatment group and a placebo group. The results are shown in the table. 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) below. Use a 0.10 significance level for both parts.
a. Test the claim that the two samples are from populations with the same mean.
What are the null and alternative hypotheses?
OA. Ho: H₁ H₂
H₁: H₁ H₂
C
OC. Ho: H₁ H₂
H₁ H₁ H₂
OB. Ho: H₁ H₂
H₁: H₁ H₂
OD. Ho HH
H₁: H₁2H₂
u
n
X
S
Treatment Placebo
Hy
H₂
27
38
2.36
2.63
0.56
0.94
Transcribed Image Text:A study was done using a treatment group and a placebo group. The results are shown in the table. 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) below. Use a 0.10 significance level for both parts. a. Test the claim that the two samples are from populations with the same mean. What are the null and alternative hypotheses? OA. Ho: H₁ H₂ H₁: H₁ H₂ C OC. Ho: H₁ H₂ H₁ H₁ H₂ OB. Ho: H₁ H₂ H₁: H₁ H₂ OD. Ho HH H₁: H₁2H₂ u n X S Treatment Placebo Hy H₂ 27 38 2.36 2.63 0.56 0.94
a. Test the claim that the two samples are from populations with the same mean.
What are the null and alternative hypotheses?
OA. Ho: #₁ #1₂
H₁: Hy <H₂
OC. Ho: #₁ #₂
H₁: 1₂*1₂
The test statistic, t, is (Round to two decimal places as needed.)
The P-value is (Round to three decimal places as needed.)
State the conclusion for the test.
OB. Ho: #₁ <H₂
H₁: Hy 2H₂
OD. Ho: #₁=4₂
H₁: Hy> #₂
A. Reject the null hypothesis. There is not sufficient evidence to warrant rejection of the claim that the two samples are from populations with the same mean.
B. Reject the null hypothesis. There is sufficient evidence to arrant jection of the claim that the two samples are from populations with the same mean.
C. Fail to reject the null hypothesis. There is sufficient evidence to warrant rejection of the claim that the two samples are from populations with the same mean.
OD. Fail to reject the null hypothesis. There is not sufficient evidence to warrant rejection of the claim that the two samples are from populations with the same
mean.
b. Construct a confidence interval suitable for testing the claim that the two samples are from populations with the same mean.
<P₁-P₂<
(Round to three decimal places as needed.)
Transcribed Image Text:a. Test the claim that the two samples are from populations with the same mean. What are the null and alternative hypotheses? OA. Ho: #₁ #1₂ H₁: Hy <H₂ OC. Ho: #₁ #₂ H₁: 1₂*1₂ The test statistic, t, is (Round to two decimal places as needed.) The P-value is (Round to three decimal places as needed.) State the conclusion for the test. OB. Ho: #₁ <H₂ H₁: Hy 2H₂ OD. Ho: #₁=4₂ H₁: Hy> #₂ A. Reject the null hypothesis. There is not sufficient evidence to warrant rejection of the claim that the two samples are from populations with the same mean. B. Reject the null hypothesis. There is sufficient evidence to arrant jection of the claim that the two samples are from populations with the same mean. C. Fail to reject the null hypothesis. There is sufficient evidence to warrant rejection of the claim that the two samples are from populations with the same mean. OD. Fail to reject the null hypothesis. There is not sufficient evidence to warrant rejection of the claim that the two samples are from populations with the same mean. b. Construct a confidence interval suitable for testing the claim that the two samples are from populations with the same mean. <P₁-P₂< (Round to three decimal places as needed.)
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