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 1157 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	269	305	358	932
Should not	38	56	78	172
Don't know/No answer	16	15	22	53
Total	323	376	458	1157

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. Do not reject H0H0
B. Reject H0H0

Answer 1

1)

proportion of Republicans who think the full-body scans should be applied in airport=269/323=0.8328

2) proportion of Democrats who think the full-body scans should be applied in airports=0.8112

3)H0:p1=p2 ; HA:p1≠p2

4)

4)

pooled estimate of a proportion for this test =0.8212

5) standard error for this test=0.0291

6)test statistic z=0.74 ( plase try 0.75 or 0.76 if this comes wrong)

7)

p value =0.4593( please try 0.4533 or 0.4473 if this comes wrong)

8)

Do not reject H0