Question

The data for this exercise are from a sample of twelfth-graders. The students were asked how often they wear a seat belt while driving, and for this exercise, we combine the responses for "never" and "rarely" and for "most times" and "always" and ignore the "sometimes" responses. A contingency table of the results for males and females follows.

Seat Belt Use
	Most Times or Always	Rarely or Never	Total
Female	964	101	1065
Male	914	269	1183
Total	1878	370	2248

(a) Calculate the row percentages for females and the row percentages for males.(Round all answers to the nearest tenth.)

	Most Times or Always	Rarely or Never
Female	%	%
Male	%	%

Compare them.
In the sample, females were  ---Select--- more less likely to wear a seat belt. But can this be applied to the entire population? The way to tell is to run the Test of Independence.

(b) Specify the null and alternative hypotheses that could be tested by using a chi-square statistic in this situation.

Null hypothesis.
H₀: Gender and seat belt use are  ---Select--- independent (not related; no difference in the row %'s) dependent (related; significant difference in the row %'s) for the population of 12^th graders.

Alternative hypothesis.
H_a: Gender and seat belt use are ---Select--- dependent (related) independent (not related) for the population of 12^th graders.

(c) Calculate the expected count, E, for the cell "Male, Most times or Always." (Round the answer to the nearest hundredth.)
E = ______

(d) Using the expected count you calculated in part (c), obtain the expected counts for the remaining cells by subtraction. Remember that row and column totals are the same for expected counts as they are for observed counts. (Round all answers to the nearest hundredth.)

	Most Times or Always	Rarely or Never
Female	___________________	______________
Male	___________________	______________

(e) Compute the chi-square statistic, χ ². (Round your answer to the nearest hundredth.)
χ ² =  
________
(f) Use the chi-square statistic computed in part (e) to find a p-value. (Round the answer to the nearest hundredth.)
p =  
__________
(g) Form a conclusion in the context of the situation. Be sure to state the level of significance you are using.
Using any reasonable α, the null hypothesis ---Select--- can cannot be rejected. We can conclude that there is. ---Select--- not a relationship a relationship between gender and seat belt use. Meaning: there's a difference in the percentage of all male 12th graders that wear their seat belts while driving are different than than for all female 12th graders.

Answer 1