Question

You wonder whether men or women are more likely to be driving when both a man and a woman are in the front seat of a car. You observe 20 cars with both a man and a woman in the front seat and count how many times the man is driving. Of the 20 cars you observed, the man was driving in 15 of them. What is the probability value for this result? (Give your answer to at least 3 places past the decimal point) Selected Answer: 0.75 Response Feedback: Incorrect, Review Chapter 11, the Logic of Hypothesis Testing Note that you will need to use Excel or the binomial calculator for this problem http://onlinestatbook.com/2/java/binomialProb.html Note that this is a 2-tailed test because you asked whether men or women were more likely to be driving. Make sure you include both tails.

Answer 1

Total number of cars observed = 20 Number of times man was driving = 15 So, sample proportion of men drivin -0.75 If men and women are equally likely to drive, then the null and alternative hypothesis will be formulated as follows: Ho: p=0.5 H:p0.5 To test the above hypothesis, a z-test for single proportion is to be conducted. The test statistic is computed by the following formula: P-Po P. (1-P) 0.75 -0.50 0.50×(1-0.50) V20 = 2.24 The p-value for the above test statistic at 5% level of significance is computed using MS- Excel function as shown in the screenshot below:

fp =2*(1-NORM.S.DIST(2.24,TRUE)) The p-value is obtained as 0.025. As the p-value is less than 0.05, so the null hypothesis will be rejected at 5% level of significance. Therefore, there is sufficient evidence to conclude that men are more likely to drive than women.