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Chapter 10: Problem 44

For which of the following combinations of \(P\) -value and significance level would the null hypothesis be rejected? a. \(P\) -value \(=0.426 \quad \alpha=0.05\) b. \(P\) -value \(=0.033 \quad \alpha=0.01\) c. \(P\) -value \(=0.046 \quad \alpha=0.10\) d. \(P\) -value \(=0.026 \quad \alpha=0.05\) e. \(P\) -value \(=0.004 \quad \alpha=0.01\)

Short Answer

Expert verified
Based on the comparison of P-values with their respective alpha levels, the null hypothesis would be rejected only in cases c, d, and e.

Step by step solution

01

Compare P-value and Alpha for Case a

In case a, P-value is equal to 0.426 and alpha is 0.05. Since the P-value is larger than alpha, the null hypothesis would not be rejected.
02

Compare P-value and Alpha for Case b

In case b, P-value is equal to 0.033 and alpha is 0.01. Again the P-value is larger than alpha, so the null hypothesis would not be rejected.
03

Compare P-value and Alpha for Case c

In case c, P-value is 0.046 and alpha is 0.10. Now, the P-value is smaller than alpha, so the null hypothesis would be rejected in this case.
04

Compare P-value and Alpha for Case d

In case d, P-value is 0.026 and alpha is 0.05. Here, the P-value is smaller than alpha so the null hypothesis would be rejected.
05

Compare P-value and Alpha for Case e

Finally, in case e, P-value is 0.004 and alpha is 0.01. In this case as well, the P-value is smaller than alpha, hence the null hypothesis would be rejected.

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Most popular questions from this chapter

Explain why a \(P\) -value of 0.0002 would be interpreted as strong evidence against the null hypothesis.

The article "Poll Finds Most Oppose Return to Draft, Wouldn't Encourage Children to Enlist" (Associated Press, December 18,2005 ) reports that in a random sample of 1,000 American adults, 700 indicated that they oppose the reinstatement of a military draft. Suppose you want to use this information to decide if there is convincing evidence that the proportion of American adults who oppose reinstatement of the draft is greater than two-thirds. a. What hypotheses should be tested in order to answer this question? b. The \(P\) -value for this test is \(0.013 .\) What conclusion would you reach if \(\alpha=0.05 ?\)

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Suppose that for a particular hypothesis test, the consequences of a Type I error are very serious. Would you want to carry out the test using a small significance level \(\alpha\) (such as 0.01 ) or a larger significance level (such as 0.10 )? Explain the reason for your choice.
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