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	[ Select ]                       ["79.03", "71.22", "77.03", "69.22"]	[ Select ]                       ["79.05", "70.25", "77.41", "74.97"]
Disagree	[ Select ]                       ["71.97", "72.96", "70.55", "79.65"]	[ Select ]                       ["76.21", "70.03", "71.55", "67.81"]

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

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

D) Based on this result, there                            [ Select ]                       ["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.

Answer 1

Applying chi square test of independence:

A)

Ei=row total*column total/grand total	3 or less	more than 3
Agrree	77.03	74.97
disagree	71.97	70.03

B)

test statistic X2 =

1.346

C)

degree of freedom(df) =(rows-1)*(columns-1)=		1
for 1 df and 0.1 level , critical value       χ2=		2.706

D)

since test statistic <critical value :

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.