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.
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 =(x_{1}+x_{2})/(n_{1}+n_{2})= | 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
Get Answers For Free
Most questions answered within 1 hours.