QUESTION 22 Progressive Insurance would like to test the hypothesis that a diffe

Question

QUESTION 22 Progressive Insurance would like to test the hypothesis that a difference exists in the proportion of students in 12th grade who text while driving when compared to the proportion of 11th grade drivers who text. A random sample of 160 12th grade students found that 84 texted while driving. A random sample of 175 11th grade students found that 70 texted while driving. if Population 1 is defined as 12th grade drivers and Population 2 is defined as 1 1 th grade drivers, and using a 0.05, the conclusion for this hypothesis test would be that because the absolute value of the test statistic is A. more than the absolute value of the critical value, Progressive Insurance can conclude that a difference exists in the proportion of B. less than the absolute value of the critical value, Progressive Insurance can conclude that a difference exists in the proportion of students C. more than the absolute value of the critical value, Progressive Insurance cannot conclude that a difference exists in the proportion of D. less than the absolute value of the critical value, Progressive Insurance cannot conclude that a difference exists in the proportion of students in 12th grade who text while driving when compared to the proportion of 11th grade drivers who text in 12th grade who text while driving when compared to the proportion of 11th grade drivers who text students in 12th grade who text while driving when compared to the proportion of 11th grade drivers who text students in 12th grade who text while driving when compared to the proportion of 11th grade drivers who text

Explanation / Answer

28)

p1 = 126/200 = 0.63 , n1 = 200 , p2= 119/175 = 0.68, n2 = 175

z value at 98% CI = 2.33

CI = (p1 - p2) +/- z * sqrt(p1 * ( 1 -p1)/n1 + p2 * (1 -p2)/n2)
= ( 0.63 - 0.68) + /- 2.33 * sqrt( (0.63 * 0.37) / 200 + (0.68 * 0.32)/175)
= (-0.164 , 0.064)

answer is option B)

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