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 1114 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	258	293	344	895
Should not	37	54	75	166
Don't know/No answer	16	15	22	53
Total	311	362	441	1114

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. ?0:?1=?2H0:p1=p2 ; ??:?1≠?2HA:p1≠p2
B. ?0:?1=?2H0:p1=p2 ; ??:?1>?2HA:p1>p2
C. ?0:?1=?2H0:p1=p2 ; ??:?1<?2HA: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. Based on the p-value, we have:
A. little evidence
B. extremely strong evidence
C. strong evidence
D. very strong evidence
E. some evidence
that the null model is not a good fit for our observed data.

Answer 1

1) proportion of Republicans who think the full-body scans should be applied in airports =25/311=0.8296

2) proportion of Democrats who think the full-body scans should be applied in airports =293/362=0.8094

3) A. ?0:?1=?2H0:p1=p2 ; ??:?1≠?2HA:p1≠p2

4)

pooled prop p̂ =(x1+x2)/(n1+n2)=

0.8187

5)

std error Se=√(p̂1*(1-p̂1)*(1/n1+1/n2) =

0.0298

6)

test stat z=(p̂1-p̂2)/Se =

0.6778

7)

P value   =

0.4979

8)\

A. little evidence