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 1106 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 | 343 | 891 |
Should not | 37 | 53 | 74 | 164 |
Don't know/No answer | 15 | 15 | 21 | 51 |
Total | 309 | 359 | 438 | 1106 |
We want to test to determine if party affiliation and opinion are
independent using the hypotheses:
H0:H0: Party affiliation and opinion are independent
HA: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. extremely strong evidence
B. strong evidence
C. very strong evidence
D. little evidence
E. some evidence
that the null model is not a good fit for our observed data.
The statistic software output for this problem is:
(a)
Expected value = (309 * 891) / 1106 = 248.9322
(b) = 3.7255
(c)degrees of freedom = 4
(d) p-value = 0.4444
(e) little evidence
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