Question

While nearly all toddlers and preschool-age children eat breakfast daily, consumption of breakfast dips as children grow older. The Youth Risk Behavior Surveillance System (YRBSS) monitors health risk behaviors among U.S. high school students, which include tobacco use, alcohol and drug use, inadequate physical activity, unhealthy diet, and risky sexual behavior. In 2015, the survey randomly selected 3470 9th-graders and 3301 12th-graders and asked them if they had eaten breakfast on all seven days before the survey.15 Of these students, 1374 9th-graders and 1116 12th-graders said Yes. Do these data give evidence that the proportion of 12th-graders who eat breakfast daily is lower that the proportion of 9th-graders eating breakfast daily? Exercises 23.9 through 23.13 are based on these results.

The numerical value of the z statistic for comparing the proportions of 9th- and 12th-graders who ate breakfast daily is

a) 2.45.

b) 3.78.

c) z = 4.94.

Answer 1

Correct option:

(c)    Z = 4.94

Explanation:

Question asked: The numerical value of the z statistic for comparing the proportions of 9th- and 12th-graders who ate breakfast daily

n1 = 3470

p1 = 1374/3470 = 0.396

n2 = 3301

p2 = 1116/3301 = 0.3381

Pooled Proportion is got as follows:

So,

Test Statistic Z is given by: