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? Which of the following is the correct value of the test statistic? A) z = −0.9804 B) t₁₀₉₈ = −0.9804 C) z = 0.9804 D) t₁₀₉₈ = 0.9804

Question

Quizplus · Accepted Answer

We can use a two-sample z-test for comparing the proportions of lost bags in the two airlines. The null hypothesis is that the population proportions are equal, and the alternative hypothesis is that the population proportion of lost bags is higher for Standard Air. The test statistic is calculated as:

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

where p1 = 45/600 = 0.075, p2 = 30/500 = 0.06, n1 = 600, n2 = 500, and p_pool = (45 + 30) / (600 + 500) = 0.066.

Plugging in the values, we get:

z = (0.075 - 0.06) / sqrt(0.066 * 0.934 * (1/600 + 1/500)) ≈ 0.9804

Since we are testing for a higher proportion in Standard Air (one-tailed test), the p-value is the area to the right of z = 0.9804 under the standard normal distribution. This can be looked up in a standard normal table or calculated using software, and is approximately 0.163.

Since this p-value is higher than the significance level of 0.05, we fail to reject the null hypothesis and conclude that there is not enough evidence to say that Standard Air has a higher population proportion of lost bags on international flights than Down Under airlines. Thus, the correct answer is C, and the value of the test statistic is z = 0.9804.

A Consumer Magazine Wants to Figure Out Which of Two