Question

Suppose you are conducting a test of significance with the null hypothesis that your cat Cayce will pick the correct cancer specimen 25% of the time and the alternative hypothesis is that he will pick the cancer specimen at a rate different than 25%. You obtain a p-value of 0.07. You also construct 95% and 99% confidence intervals from your data. What will be true about your confidence intervals?

A. Both the 95% and the 99% intervals will contain 0.25.

B. Neither the 95% nor the 99% intervals will contain 0.25.

C. The 95% interval will contain 0.25, but the 99% interval will not contain 0.25.

D. The 95% interval will not contain 0.25, but the 99% interval will contain 0.25.

Answer 1

The p-value is 0.07, indicating that we fail to reject the null hypothesis. Both the 95% and 99% confidence intervals will contain 0.25.

Step-by-step explanation:

The p-value is the probability of observing a test statistic as extreme as the one obtained, assuming that the null hypothesis is true. In this case, the p-value is 0.07. Since the p-value is greater than the significance level of 0.05, we fail to reject the null hypothesis. This means that there is not enough evidence to conclude that Cayce picks the cancer specimen at a rate different than 25%.

The 95% confidence interval is calculated by taking the point estimate plus and minus the margin of error. Since the null hypothesis is that Cayce picks the correct cancer specimen 25% of the time, the point estimate is 0.25. The margin of error can be calculated using the formula: margin of error = critical value * standard error, where the critical value is determined based on the desired level of confidence and the standard error is calculated using the sample proportion. The 99% confidence interval is wider than the 95% confidence interval because it includes a larger range of values to capture.

Based on the p-value and the fact that we fail to reject the null hypothesis, it is likely that both the 95% and the 99% confidence intervals will contain 0.25. Therefore, the correct answer is A. Both the 95% and the 99% intervals will contain 0.25.