Question

nnncing voters: Is a Phone Call Better than a Flyer? variable is the proportion of voters planning to vote for the candidate, with pi and p recelving a fyer, respectively.) The sample statistic of interest is p-ps We are testing Ho :Ph to investigate whether a recorded phone call is more effective than a fiyer in persuading voters to vote for a particular candidate. The response planning to vote for the candidate, with Pi and p representing the proportions for the two methods (receiving a phone call and proportions, p1-P for this test is shown in the figure below. vs H Pi> P2.A randomization distribution of differences in 120 100 60 40 20 -06 0.4 0.2 0.0 Difference 0.2 0.4 0.6 (a) Four possible sample statistics are given, along with four possible p-values. Match the statistics with the p-values. 1.p-0.11 p-value:

Answer 1

1) The hypothesis testing problem is

$H_0:p_1-p_2=0$ Vs $H_0:p_1-p_2>0$

a.

$H_0:\hat{p_1}-\hat{p_2}=0.11$

The pvalue is P(Z>0.11)=1-P(Z<=0.11)

=0.5438 ## By using R command > 1-pnorm(0.11,0,1)

b)

$H_0:\hat{p_1}-\hat{p_2}=0.33$

The pvalue is P(Z>0.33)=1-P(Z<=0.33)

=0.3707 ## By using R command > 1-pnorm(0.33,0,1)

c)

$H_0:\hat{p_1}-\hat{p_2}=0.52$

The pvalue is P(Z>0.52)=1-P(Z<=0.52)

=0.3015 ## By using R command > 1-pnorm(0.52,0,1)

d)

$H_0:\hat{p_1}-\hat{p_2}=0.73$

The pvalue is P(Z>0.73)=1-P(Z<=0.73)

=0.2327 ## By using R command > 1-pnorm(0.73,0,1)

b) Of the four values given in part a) The P value 0.001 provides the strongest evidence that a phone call is more effective. Since Pvalue 0.001 indicate the rejection of the null hypothesis at 1%,5% as well as 10% level of significance.