Question

According to a Washington Post-ABC News poll, 331 of 502 randomly selected American adults said they would not be bothered if the National Security Agency collected records of personal telephone calls. The data were used to test \(H_{0}: p=0.5\) versus \(H_{a}: p>0.5,\) and the null hypothesis was rejected. a. Based on the hypothesis test, what can you conclude about the proportion of American adults who would not be bothered if the National Security Agency collected records of personal telephone calls? b. Is it reasonable to say that the data provide strong support for the alternative hypothesis? c. Is it reasonable to say that the data provide strong evidence against the null hypothesis?

Short answer

a. The proportion of American adults who would not be bothered if the National Security Agency collected records of personal telephone calls is greater than 0.5. b. It's not reasonable to say that the data provide strong support for the alternative hypothesis without additional information like p-value or confidence level. c. Because the null hypothesis was rejected, it's reasonable to suggest that the data provides evidence against the null hypothesis.

Step-by-step solution

Reviewing the hypothesis test results

Given the problem statement, it’s known that the null hypothesis was rejected, and therefore we can conclude that \(p> 0.5\). More than half of American adults would not be bothered if the NSA collected records of their personal calls.

Conclusion based on the hypothesis test

Based on the hypothesis test results, it can be concluded that there is sufficient evidence to believe that more than half of American adults would not be bothered if the NSA collected records of their personal calls. Hence, the proportion of American adults who would not be disturbed by this action is significantly greater than 0.5.

Determining if the data provides strong evidence

Since the null hypothesis was rejected, this suggests that the data does provide some evidence supporting the alternative hypothesis (\(H_{a}: p>0.5\)). However, without knowledge of the test statistic, p-value, or confidence level, it's not reasonable to say if it's a strong or weak support. As having these data points will provide quantitative measures of the evidence.

Evaluating the data against the null hypothesis

Hypothesis testing helps determine if there is enough statistical evidence in favor of a certain belief, or hypothesis, about a parameter. In this case, since null hypothesis (\(H_{0}: p=0.5\)) was rejected, it's reasonable to say that the data provides evidence against the null hypothesis.