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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

The authors of the article "Perceived Risks of Heart Disease and Cancer Among Cigarette Smokers" (Journal of the American Medical Association [1999]: \(1019-1021\) ) expressed the concern that a majority of smokers do not view themselves as being at increased risk of heart disease or cancer. A study of 737 current smokers found that only 295 believe they have a higher than average risk of cancer. Do these data suggest that \(p,\) the proportion of all smokers who view themselves as being at increased risk of cancer, is less than \(0.5,\) as claimed by the authors of the paper? For purposes of this exercise, assume that this sample is representative of the population of smokers. Test the relevant hypotheses using \(\alpha=0.05\)

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