Question

Influencing Voters Exercise 4.39 on page 272 describes a possible study to see if there is evidence that a recorded phone call is more effective than a mailed flyer in getting voters to support a certain candidate. The study assumes a significance level of \(\alpha=0.05\) (a) What is the conclusion in the context of thisstudy if the p-value for the test is \(0.027 ?\) (b) In the conclusion in part (a), which type of error are we possibly making: Type I or Type II? Describe what that type of error means in this situation. (c) What is the conclusion if the p-value for the test is \(0.18 ?\)

Short answer

(a) There is significant evidence to suggest that the recorded phone call is more effective than a mail flyer. (b) In this case, we could be making a Type I error, i.e., wrongly concluding that the recorded phone call is more effective. (c) The data does not provide enough evidence to suggest that a recorded phone call is more effective.

Step-by-step solution

Understanding p values and statistical significance

The p-value is the probability that the results of your test occurred randomly when the null hypothesis is true. If the p-value is greater than the set significance level (\(\alpha\)), we fail to reject the null hypothesis. If the p-value is less than or equal to the significance level, we reject the null hypothesis in favour of the alternative hypothesis.

Compare p value and significance level for part (a)

For the first part of this question, the p-value is \(0.027\), which is less than our significance level \(\alpha=0.05\). This means we reject the null hypothesis. Therefore, there is significant evidence to suggest that a recorded phone call is more effective than a mail flyer in getting voters to support a certain candidate.

Understand Type I and Type II errors

In statistical hypothesis testing, a type I error is the rejection of a true null hypothesis, while a type II error is failing to reject a false null hypothesis. Put simply, a type I error means making the wrong call when the null is true, and a type II error means making the wrong call when the alternative is true.

Identify type of error in part (a)

Since we have rejected the null hypothesis in part (a), we could possibly be making a Type I error. A Type I error in this context means concluding that a recorded phone call is more effective, when in fact, there is no difference in effectiveness between the two methods.

Compare p value and significance level for part (c)

In the final part of the question, the p-value is \(0.18\), which is higher than the significance level \(\alpha = 0.05\). So, we fail to reject the null hypothesis. This means that the available data does not provide enough evidence to conclude that a recorded phone call is more effective than a mailed flyer.