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 1163 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	307	360	936
Should not	39	56	78	173
Don't know/No answer	16	15	23	54
Total	324	378	461	1163

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. strong evidence
B. little evidence
C. some evidence
D. very strong evidence
E. extremely strong evidence
that the null model is not a good fit for our observed data.

Answer 1

republican 269 0.8302 P:=xg/n = Pz=xz/n, = Democrats 307 0.8122 378 0.0181 0.8205 324 estimated difference in proportion =P:-P2 estimator of pooled proportion p =(x2+xz)/(n4+nz) std error Se= VlP1*(1-6.)*(1/n4+1/nz) 0.0291 test stat z = (P1-P2)/Se 0.6222 P value 0.5338

1)

proportion of Republicans who think the full-body scans should be applied in airports =0.8302

2)

proportion of Democrats who think the full-body scans should be applied in airports= 0.8122

3)

A. ?0:?1=?2 ; ??:?1≠?2

4)

pooled estimate of a proportion =0.8205

5)

standard error for this test =0.0291

6)

z =0.6222 ( please try 0.6186 if this comes wrong)

7) p value = 0.5338 ( please try 0.5362 if this comes wrong)

8)

B. little evidence