Question

In a survey of 3135 adults in a​ nation, a poll asked people whether they smoked cigarettes and whether they always wear a seat belt in a car. The table available below shows the results of the survey. For each​ activity, we define a success as finding an individual who participates in the hazardous activity. Complete parts​ (a) and​ (b) below. LOADING... Click the icon to view the survey results. ​(a) Why is this a dependent​ sample? A. This is a dependent sample because the two responses for each question are mutually exclusive. B. This is a dependent sample because the values in the table depend on the responses to the question. C. This is a dependent sample because the two variables are measured on the same individual. D. This is a dependent sample because the two variables are not mutually exclusive. ​(b) Is there a significant difference in the proportion of individuals who smoke and the proportion of individuals who do not wear a seat​ belt? In other​ words, is there a significant difference between the proportion of individuals who engage in hazardous​ activities? Use the alphaequals0.10 level of significance. Let p 1 represent the proportion who smoke and p 2 represent the proportion who do not wear a seat belt. What are the null and alternative​ hypotheses? A. Upper H 0 : p 1 equals p 2 Upper H 1 : p 1 not equals p 2 B. Upper H 0 : p 1 not equals p 2 Upper H 1 : p 1 equals p 2 C. Upper H 0 : p 1 equals p 2 Upper H 1 : p 1 greater than p 2 D. Upper H 0 : p 1 equals p 2 Upper H 1 : p 1 less than p 2 Calculate the test statistic. chi Subscript 0 Superscript 2equals nothing ​(Round to two decimal places as​ needed.) Find the​ P-value for the test statistic. The​ P-value is nothing. ​(Round to three decimal places as​ needed.) Test the null hypothesis. Choose the correct conclusion below. A. Do not reject the null hypothesis because there is not sufficient evidence to conclude that the proportion who smoke is greater than the proportion who do not wear a seat belt. B. Do not reject the null hypothesis because there is not sufficient evidence to conclude that the proportion who smoke and the proportion who do not wear a seat belt are different. C. Reject the null hypothesis because there is sufficient evidence to conclude that the proportion who smoke is less than the proportion who do not wear a seat belt. D. Reject the null hypothesis because there is sufficient evidence to conclude that the proportion who smoke and the proportion who do not wear a seat belt are different. Click to select your answer(s).

	No Seat Belt ​(success)	Seat Belt ​(failure)
Smoke​ (success)	77	467
Do Not Smoke​ (failure)

340 2251

Answer 1

(a)

C. This is a dependent sample because the two variables are measured on the same individual.

(B)

Hypotheses are:

(C)

Following is the output of chi square test statistics:

Chi-square Contingency Table Test for Independence
			No Seat Belt ​(success)	Seat Belt ​(failure)	Total
	Smoke​ (success)		77	467	544
	Do Not Smoke​ (failure)		340	2251	2591
	Total		417	2718	3135
			.42	chi-square
			1	df
			.5193	p-value

The chi square test statistics is

The p-value is: 0.5193

Since p-value is large so we fail to reject the null hypothesis.

Correct option:

B. Do not reject the null hypothesis because there is not sufficient evidence to conclude that the proportion who smoke and the proportion who do not wear a seat belt are different.