Question

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

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

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.

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.

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.

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.

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.