Question

(9 points) A news article reports that "Americans have differing views on two potentially inconvenient and invasive practices that airports could implement to uncover potential terrorist attacks." This news piece was based on a survey conducted among a random sample of 1123 adults nationwide, interviewed by telephone November 7-10, 2010, where one of the questions on the survey was "Some airports are now using full- body' digital x-ray machines to electronically screen passengers in airport security lines. Do you think these new x-ray machines should or should not be used at airports?" Below is a summary of responses based on party affiliation. Round all numeric answers to 4 decimal places Republican Democrat Independent Total 903 167 53 1123 296 260 37 Don't know/No answer 16 Should 347 Should not 54 76 Total 313 365 445 1. What is the proportion of Republicans who think the full-body scans should be applied in airports? 2. What is the proportion of Democrats who think the full-body scans should be applied in airports? 3. What are the correct hypotheses for a hypothesis test evaluating whether there is a difference in the proportion of Republicans and Democrats who think the full-body scans should be applied in airports? Assume that all relevant conditions are met 4. Calculate the pooled estimate of a proportion for this test. 5. Calculate the standard error for this test. 6. Calculate the test statistic for this hypothesis test. 7. Calculate the p-value for this hypothesis test

Answer 1

Ans:

1)Proportion of Republicans=260/313=0.8307

2)Proportion of Democrats=296/365=0.8110

3)option C is correct.

4)pooled proportion=(260+296)/(313+365)=0.8201

5)standard error=sqrt(0.8201*(1-0.8201)*((1/313)+(1/365)))=0.0296

6)

Test statistic:

z=(0.8307-0.8110)/0.0296

z=0.6655

*(if all exact proportions are used,then z=0.6661)

7)p-value(2 tailed)=2*P(z>0.666)=0.5057

(if exact values are used then p-value=0.5053)