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
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
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