Question

Match the four \(\mathrm{p}\) -values with the appropriate conclusion: (a) The evidence against the null hypothesis is significant, but only at the \(10 \%\) level. (b) The evidence against the null and in favor of the alternative is very strong. (c) There is not enough evidence to reject the null hypothesis, even at the \(10 \%\) level. (d) The result is significant at a \(5 \%\) level but not at a \(1 \%\) level. I. 0.00008 II. 0.0571 III. 0.0368 IV. \(\quad 0.1753\)

Short answer

(a) - II, (b) - I, (c) - IV, (d) - III

Step-by-step solution

Link p-values to Conclusions

Option I, a p-value of 0.00008, is a very small p-value, indicating strong evidence against the null hypothesis. So, it matches with (b) - The evidence against the null and in favor of the alternative is very strong. Option II, a p-value of 0.0571 indicates that the evidence against the null hypothesis is not strong enough at the 5 % level, but significant at the 10 % level, thus, matching with (a) - The evidence against the null hypothesis is significant, but only at the 10 % level. Option III, a p-value of 0.0368, is significant at the 5% level but not at the 1% level, which matches with (d) - The result is significant at a 5% level but not at a 1% level. Lastly, option IV, a p-value of 0.1753, is not small enough to provide enough evidence against the null hypothesis, even at the 10% level, which matches with (c) - There is not enough evidence to reject the null hypothesis, even at the 10 % level.