Question

A survey of adults was conducted in which the subjects were asked whether they agree that the government should prohibit smoking in public places. In addition, each subject was asked how many people lived in their household. The results are summarized in the following contingency table. Use a 0.1 significance level to test for independence between the two variables.

	3 or less	More than 3
Agree	82	70
Disagree	67	75

A) Calculate the Table of Expected Values:

	3 or less	More than 3
Agree	["69.22", "71.22", "77.03", "79.03"]	["74.97", "70.25", "79.05", "77.41"]
Disagree	["72.96", "79.65", "70.55", "71.97"]	["67.81", "70.03", "71.55", "76.21"]

B) Calculate the Chi-Squared test statistic: ["1.346", "0.158", "2.826", "1.968", "1.789"]           

C) Calculate the Critical Value:   ["5.024", "7.879", "2.706", "3.841", "6.635"]           

D) Based on this result, there   ["does", "does not"] appear to be enough evidence to support the claim that the number of people in a household is independent of their view on smoking in public areas.

**NOTE the values in-between " " are possible answer choices

Answer 1

(A)

H0: Null Hypothesis: The variables: whether they agree that the government should prohibit smoking in public places and number of people lived in their household are independent (Claim)

HA: Alternative Hypothesis: The variables: whether they agree that the government should prohibit smoking in public places and number of people lived in their household are dependent

Observed Frequencies:

	3 or less	More than 3	Total
Agree	82	70	152
Disagree	67	75	142
Total	149	145	294

Expected Frequencies:

	3 or less	More than 3	Total
Agree	149 X 152/ 294 = 77.034	145 X 152/ 294 = 74.966	152
Disagree	149 X 142/ 294 = 71.966	145 X 142/ 294 = 70.034	142
Total	149	145	294

So, Answer is:

	3 or less	More than 3
Agree	77.03	74.97
Disagree	71.97	70.03

(B)

The Chi-Squared test statistic is got as follows:

Observed (O)	Expected (E)	(O - E)2/E
149	77.034	0.320
70	74.966	0.329
67	71.966	0.343
75	70.034	0.352
Total =		1.346

So,

Correct option:

1.346

(C)

= 0.10

df = (2 - 1) X (2 - 1) = 1

From Table, critical value of = 2.706

So,

Correct option:

2.706

(D)

Correct option:

Based on this result, there   does appear to be enough evidence to support the claim that the number of people in a household is independent of their view on smoking in public areas.