Question

A study of seat belt users and nonusers yielded the randomly selected sample data summarized in the given table.

Number of cigarettes smoked per day
0 1-14 15 and over

Wear seat belts 185 30 50

Don't wear seat belts 155 25 55

At the 0.01 significance level, test the claim that the amount of smoking is independent of seat belt use. Which of the following is true?

Select one:

a. The expected value of the test statistics is 13.50 and the critical value is 4.60, hence we conclude that the amount of smoking is dependent on seat belt use

b. The expected value of the test statistics is 9.21 and the critical value is 5.72, hence we conclude that the amount of smoking is dependent on seat belt use

c. The expected value of the test statistics is 4.60 and the critical value is 9.21, hence we conclude that the amount of smoking is independent of seat belt use

d. The expected value of the test statistics is 5.72 and the critical value is 4.60, hence we conclude that the amount of smoking is dependent on seat belt use

e. None of the other answers in necessary true.

f. The expected value of the test statistics is 5.72 and the critical value is 9.21, hence we conclude that the amount of smoking is independent of seat belt use

Answer 1

	Observed Frequencies
	0
0	E	G	F				Total
N	185	30	50				265
M	155	25	55				235

	Expected frequency of a cell = sum of row*sum of column / total sum
	Expected Frequencies
	E	G	F				Total
N	340*265/500=180.2	55*265/500=29.15	105*265/500=55.65				265
M	340*235/500=159.8	55*235/500=25.85	105*235/500=49.35				235

	(fo-fe)^2/fe
N	0.128	0.025	0.574
M	0.144	0.028	0.647

Chi-Square Test Statistic,χ² = Σ(fo-fe)^2/fe =   1.545

Level of Significance =   0.01
Number of Rows =   2
Number of Columns =   3
Degrees of Freedom=(#row - 1)(#column -1) = (2- 1 ) * ( 3- 1 ) =   2
  
Critical Value =   9.210

Decision: test statistic,X² < critical value , So, Do not reject the null hypothesis  

Please note that if data is correct than neither value in answer matches and hence below option can be done.

e. None of the other answers in necessary true.

Please revert back in case of any doubt.

Please upvote. Thanks in advance.