mathxd.com Statistics for the Sciences Online Course -Fall 2017 Hannah Grass | 1

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mathxd.com Statistics for the Sciences Online Course -Fall 2017 Hannah Grass | 12/7/17 10:25 PM Homework: Homework 11b Score: 0 of 8 pts Instructor-created question Save 1 of 2 (1 complete) Hw Score: 20%, 3.2 of 16 pts Question Help A study of seat belt users and nonusers yielded the randomly selected sample data summarized in the accompanying table. Use a 0.05 significance level to test the claim that the amount of smoking is independent of seat belt use. Aplausible theory is that people who smoke are less concerned about their health and safety and are therefore less inclined to wear seat belts. Is this theory supported by the sample data? Click the icon to view the data table. Determine the null and alternative hypotheses. 0 A. Ho: The amount of smoking is independent of seat belt use. 0 B. Ho: Heavy smokers are not less likely than non-smokers to wear a seat belt. ° C. More Info H The amount of smoking is not independent of seat belt use. H: Heavy smokers are less likely than non-smokers to wear a seat belt Ho: Heavy smokers are less likely than non-smokers to wear a seat belt. H: Heavy smokers are not less likely than non-smokers to wear a seat be Ho: The amount of smoking is dependent upon seat belt use. H The amount of smoking is not dependent upon seat belt use. Number of Cigarettes Smoked per Day 1-14 20 15-34 39 35 and over Wear Seat Belts 194 156 n't Wear Seat Belts D. Print Done Determine the test statistic. x2-(Round to three decimal places as needed.) Determine the P-value of the test statistic. P-ValueRound to three decimal places as needed.) Use a 0.05 significance level to test the claim that the arnount of smoking is independent of seat bel use. Aplausible theory is that people who smoke are less concerned about their health and safety and are therefore less inclined to wear seat belts. Is this theory supported by the sample data? O A. There is sufficient evidence to reject the dlaim that the amount of smoking is independent of seat belt use. The theory is not supported by the sample data. B. There is sufficient evidence to reject the dlaim that heavy smokers are less likely than non-smokers to wear a seat belt. The theory is supported by the sample data. C. There is not sufficient evidence to reject the darn that the amount of smoking is independent of seat belt use. The theory is not supported by the sample data. 0 D There is not sufficient evidence to reject the daim that heavy smokers are less likely than non-smokers to wear a seat belt. The theory is supported by the sample data. Click to select your answer(s) and then click Check Answer. Clear All Check Answer

Explanation / Answer

(A) Option A is correct in hypothesis notation.

H0: Seat belt & Smoking is independent.

Ha : Seat belt & smoking is not dependent.

(b) Now chi - square table with observed and expected value.

Observed table

Expected table

I.e.

for Wear seat belt and 0 cigarettes = Total wear * total 0 cigarettes/total population = 350*259/475 = 190.84

Expected table

Now chi -square statistic

X2= (O - E)2/E

We will evaluate the value of chi - square for each cell and then do sum of it. The chi square cell sum value is given below.

Her X2  = 1.445

P - value = CHITEST (Actual, Expected) = 0.6951

Here as p- value is greater than 0.05 so we can say that there is not sufficient evidence to reject supported by sample data. the claim that the amount of smoking is independent of seat belt use. Option C is correct.

Number of cigarettes smoked per day 0 1-14 15-34 35+ Total Wear seat belts 194 20 39 6 259 Don’t wear 156 14 41 5 216 Total 350 34 80 11 475

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