Exhibit 10.13.A consumer magazine wants to figure out which of two major airlines lost a higher proportion of luggage on international flights.The magazine surveyed Standard Air (population 1)and Down Under airlines (population 2).Standard Air lost 45 out of 600 bags.Down Under airlines lost 30 of 500 bags.Does Standard Air have a higher population proportion of lost bags on international flights? Refer to Exhibit 10.13.Calculate the value of the test statistic.

Question

Quizplus · Accepted Answer

To compare population proportions of lost luggage, we need to use a two-sample z-test. The formula for the test statistic is:

z = (p1 - p2) / sqrt(p * (1 - p) * (1/n1 + 1/n2))

where:
p1 = proportion of lost bags in population 1
p2 = proportion of lost bags in population 2
p = combined proportion of lost bags ((45+30)/(600+500) = 0.074)
n1 = sample size of population 1 (600)
n2 = sample size of population 2 (500)

Plugging in the values:
z = (0.075 - 0.06) / sqrt(0.074 * 0.926 * (1/600 + 1/500))
z = 1.23

The closest value to 1.23 is in option C.