Question

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 1140 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
Should	265	300	352	917
Should not	38	55	77	170
Don't know/No answer	16	15	22	53
Total	319	370	451	1140

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.

A. H0:p1=p2H0:p1=p2 ; HA:p1>p2HA:p1>p2
B. H0:p1=p2H0:p1=p2 ; HA:p1<p2HA:p1<p2
C. H0:p1=p2H0:p1=p2 ; HA:p1≠p2HA:p1≠p2

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.
?(z,t,X^2,F) =

7. Calculate the p-value for this hypothesis test.

8. What is your conclusion using alpha = .01

A. Reject H0H0
B. Do not reject H0H0

Answer 1

Dear student, we can provide you with four sub-questions at a time.

1) the proportion of Republicans who think the full-body scans should be applied in airports = 265/1140 = 0.2325

2) the proportion of Democrats who think the full-body scans should be applied in airports = 300/1140 =0.2632

3) since we need to check if or not there is a difference between the proportion

Hence option C is right

4) pooled estimate of proportion = (265 + 300 ) /(1140 + 1140) = 0.2478

5) standard error =