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 1102 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	256	290	341	887
Should not	37	53	74	164
Don't know/No answer	15	15	21	51
Total	308	358	436	1102

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.
?ztX^2F =

3. Calculate the degrees of freedom for this test.

4. Calculate the p-value for this hypothesis test.

5. What is your conclusion using alpha = .01

A. Reject H0H0
B. Do not reject H0H0

Answer 1

Given,

Observed Values: O

	Republican	Democrat	Independent	Total
Should	256	290	341	887
Should not	37	53	74	164
Don't know/No answer	15	15	21	51
Total	308	358	436	1102

Expected value for a given cell :

1. Expected value for the number of Republicans who think x-ray machines should be used at airports

Expected value for the number of Republicans who think x-ray machines should be used at airports = 247.9093

2. Test Statistic

O: Observed value

E: Expected value

E:Expected values	Republican	Democrat	Independent	Total
Should	(887*308)/1102	(887*358)/1102	(887*436)/1102	887
Should not	(164*308)/1102	(164*358)/1102	(164*436)/1102	164
Don't know/No answer	(51*308)/1102	(51*358)/1102	(51*436)/1102	51
Total	308	358	436	1102

E	Republican	Democrat	Independent	Total
Should	247.9093	288.1543	350.9365	887
Should not	45.8367	53.2777	64.8857	164
Don't know/No answer	14.2541	16.5681	20.1779	51
Total	308	358	436	1102

O	E	O-E	(O-E)2	(O-E)2/E
256	247.9093	8.0907	65.4601	0.2640
37	45.8367	-8.8367	78.0866	1.7036
15	14.2541	0.7459	0.5564	0.0390
290	288.1543	1.8457	3.4067	0.0118
53	53.2777	-0.2777	0.0771	0.0014
15	16.5681	-1.5681	2.4588	0.1484
341	350.9365	-9.9365	98.7336	0.2813
74	64.8857	9.1143	83.0711	1.2803
21	20.1779	0.8221	0.6759	0.0335
			Total	3.7635

Test Statistic

Test Statistic = 3.7635

3. Calculate the degrees of freedom for this test.

Degrees of freedom = (Number of rows - 1)x(Number of columns -1) = (3-1)x(3-1) =2 x 2=4

degrees of freedom for this test = 4

4. p-value for this hypothesis test

5.

alpha = .01

Conclusion:

As p-value : 0.4390 >  alpha:  .01. Don't Reject H_o

Ans:

B. Do not reject H0