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 1108 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.
Republican | Democrat | Independent | Total | |
Should | 257 | 291 | 342 | 890 |
Should not | 37 | 54 | 75 | 166 |
Don't know/No answer | 15 | 15 | 22 | 52 |
Total | 309 | 360 | 439 | 1108 |
We want to test to determine if party affiliation and opinion are
independent using the hypotheses:
?0:H0: Party affiliation and opinion are independent
??:HA: Party affiliation and opinion are not independent
Round all numeric answers to four decimal places.
1. What is the expected value for the number of Republicans who think x-ray machines should be used at airports?
2. Calculate the test statistic for this hypothesis test.
? z t X^2 F =
3. Calculate the degrees of freedom for this test.
4. Calculate the p-value for this hypothesis test.
5. Based on the p-value, we have:
A. little evidence
B. extremely strong evidence
C. some evidence
D. strong evidence
E. very strong evidence
that the null model is not a good fit for our observed data.
The statistical software output for this problem is :
expected value = 248.2
Test statistics = 4.1291
Degrees of freedom = 4
P-value = 0.3888
little evidence
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