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 1115 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	258	293	345	896
Should not	37	54	75	166
Don't know/No answer	16	15	22	53
Total	311	362	442	1115

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. some evidence
B. strong evidence
C. extremely strong evidence
D. very strong evidence
E. little evidence
that the null model is not a good fit for our observed data.

Answer 1

The statistical software output for this problem is :

Contingency table results:
Rows: var6
Columns: None

Cell format
Count (Expected count)

	R	D	I	Total
S	258 (249.92)	293 (290.9)	345 (355.19)	896
S N	37 (46.3)	54 (53.89)	75 (65.8)	166
D K	16 (14.78)	15 (17.21)	22 (21.01)	53
Total	311	362	442	1115

Chi-Square test:

Statistic	DF	Value	P-value
Chi-square	4	4.1524681	0.3858

Expected value = 249.92

Test statistics is   = 4.1525

degrees of freedom = 4

P-value = 0.3858

Conclusion : little evidence