Question

Chapter 4, Section 2, Exercise 066bd Influencing Voters: Is a Phone Call Better than a Flyer? A study is conducted to investigate whether a recorded phone call is more effective than a flyer in persuading voters to vote for a particular candidate. The response variable is the proportion of voters planning to vote for the candidate, with p1 and p2⁢ representing the proportions for the two methods (receiving a phone call and receiving a flyer, respectively.) The sample statistic of interest is p^1-p^2. We are testing H0:p1=p2vs Ha:p1>p2. A randomization distribution of differences in proportions, p^1-p^2, for this test is shown in the figure below.

(a) Four possible sample statistics are given, along with four possible p-values. Match the statistics with the p-values. 1. p^1-p^2=0.15 p-value: 0.001 0.310 0.011 0.086 2. p^1-p^2=0.33 p-value: 0.310 0.011 0.001 0.086 3. p^1-p^2=0.50 p-value: 0.011 0.086 0.001 0.310 4. p^1-p^2=0.70 p-value: 0.086 0.310 0.011 0.001

(b) Of the four values given in part (a), which provides the strongest evidence that a phone call is more effective? p-value =0.310 p-value =0.001 p-value =0.011 p-value =0.086

Answer 1

We are testing H0:p1=p2vs Ha:p1>p2

that is H0:p1 - p2 = 0 vs Ha:p1 - p2 > 0

P-value depends on test statistic which depends on $\hat{p_1}-\hat{p_2}$ . A large value of test statistic or $\hat{p_1}-\hat{p_2}$ will give low values of p-values.

For largest value of $\hat{p_1}-\hat{p_2}$ = 0.70, p-value will be lowest which is 0.001

The second largest value of $\hat{p_1}-\hat{p_2}$ = 0.50, p-value will be second lowest which is 0.011

Similarly, p-value for $\hat{p_1}-\hat{p_2}$ = 0.33 is 0.086 and for $\hat{p_1}-\hat{p_2}$ = 0.15 is 0.310

Thus, the correct answers are

1. p^1-p^2=0.15 p-value: 0.310
2. p^1-p^2=0.33 p-value: 0.086
3. p^1-p^2=0.50 p-value: 0.011
4. p^1-p^2=0.70 p-value: 0.001

(b)

The strongest evidence that a phone call is more effective is provided by the lowest value of p-value which gives sufficient evidence that phone call is more effective at significance level of 0.001 and confidence level of 1 - 0.001 = 0.999

p-value =0.001