Question

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.

Answer 1

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