Question

Chapter 4, Section 5, Exercise 160

Hypotheses for a statistical test are given, followed by several possible confidence intervals for different samples. In each case, use the confidence interval to state a conclusion of the test for that sample and give the significance level used. In addition, in each case for which the results are significant, state which group (1 or 2) has the larger mean.

Hypotheses: H0:μ1=μ2 vs Ha:μ1≠μ2

(a) 95% confidence interval for μ1-μ2: 0.15 to 0.55

Conclusion:

RejectDo not reject H0

Significance level:

99%10%1%5%95%90%

Group with the larger mean:

Group 1 Group 2 Cannot determine

(b) 99% confidence interval for μ1-μ2: -2.2 to 5.6

Conclusion:

RejectDo not reject

H0

Significance level:

10%95%5%1%99%90%

Group with the larger mean:

Group 2Group 1Cannot determine

(c) 90% confidence interval for μ1-μ2: -10.8 to -3.7

Conclusion:

RejectDo not reject

H0

Significance level:

5%1%99%90%95%10%

Group with the larger mean:

Group 1Group 2Cannot determine

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Answer 1

(a)

Given:

Hypotheses: H0:μ1=μ2 vs Ha:μ1≠μ2

95% confidence interval for μ1-μ2: 0.15 to 0.55

(i)

Conclusion:

Reject   H0

Reason: All values in the confidence interval are positive

(ii)

Significance level:

5%

(iii)

Group with the larger mean:

Group 1

Reason: All values in the confidence interval are positive

(b)

Given:

99% confidence interval for μ1-μ2: -2.2 to 5.6

(i)

Conclusion:

Do not reject H0

Reason: Confidence Interval includes 0

(ii)

Significance level:

1%

(iii)

Group with the larger mean:

Cannot determine

Reason: Confidence Interval includes 0

(c)
Given:

90% confidence interval for μ1-μ2: -10.8 to -3.7

(i)

Conclusion:

Reject H0

Reason: All values in the confidence interval are negative.

(ii)
Significance level:

10%

(iii)

Group with the larger mean:

Group 2

Reason: All values in the confidence interval are negative.