Questions: In hypothesis testing, does choosing between the critical value method or the P-value method affect your conclusion? Explain. Choose the correct answer below. A. Yes, because the critical value method uses critical value(s) to identify the rejection region(s). The P-value method compares the P -value with the level of significance α. B. No, because both methods involve comparing the standardized test statistic with the rejection region(s). C. Yes, because the P-value method is more accurate than the critical value method. D. Yes, because the critical value method is more accurate than the P -value method. E. No, because both involve comparing the test statistic's probability with the level of significance.

Solution Steps

The critical value method involves determining the critical value(s) from the distribution of the test statistic based on the significance level \( \alpha \). The rejection region is defined by these critical values, and the test statistic is compared to this region to decide whether to reject the null hypothesis.

The P-value method calculates the probability of observing a test statistic as extreme as, or more extreme than, the one observed, assuming the null hypothesis is true. This P-value is then compared to the significance level \( \alpha \) to decide whether to reject the null hypothesis.

Both methods ultimately lead to the same conclusion because they are based on the same underlying principles of hypothesis testing. The critical value method uses the rejection region, while the P-value method uses the probability of the test statistic. However, both involve comparing the test statistic (or its probability) to the significance level \( \alpha \). Therefore, the choice between the two methods does not affect the conclusion.

Final Answer