Question

Research states the 30% of parents spank their toddlers. You decide to test this claim at a level of significance of 0.05 and randomly survey 1000 parents of toddlers. You find the 95% confidence interval to be (0.22, 0.26). From this confidence interval you decide which of the following:

A. Fail to accept the alternative hypothesis
B. Reject the null hypothesis since the claim is not in the confidence interval
C. Accept the alternative hypothesis
D. Fail to reject the null hypothesis because you cannot use the confidence interval to determine the decision

Answer 1

The correct decision based on the provided confidence interval is to reject the null hypothesis since the claim of 30% is not within the interval (0.22, 0.26).

Step-by-step explanation:

Given the 95% confidence interval (0.22, 0.26) for the proportion of parents who spank their toddlers, we compare this interval to the claim that 30% of parents spank their toddlers. Since 0.30 is not within the interval (0.22, 0.26), the population proportion that is suggested by the claim is not in the confidence interval. With a level of significance of 0.05, the appropriate action here is to reject the null hypothesis because our confidence interval suggests that the true proportion is likely between 22% and 26%, which does not include the claimed 30%.

To reject the null hypothesis means that there is statistically significant evidence to suggest that the true proportion of parents who spank their toddlers is different from the claimed 30%. Thus, the correct choice from the given options would be B. Reject the null hypothesis since the claim is not in the confidence interval.