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 38 out of 510 bags. Down Under airlines lost 28 of 460 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?Multiple Choicez = 0.842t968 = 0.842z = −0.842t968 = −0.842
Question
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 38 out of 510 bags. Down Under airlines lost 28 of 460 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?Multiple Choicez = 0.842t968 = 0.842z = −0.842t968 = −0.842
Solution
To answer this question, we first need to calculate the proportion of lost bags for each airline.
For Standard Air, the proportion (p1) is 38/510 = 0.0745.
For Down Under airlines, the proportion (p2) is 28/460 = 0.0609.
Next, we calculate the pooled proportion (p), which is the total number of lost bags divided by the total number of bags. This is (38+28) / (510+460) = 66/970 = 0.0680.
The standard error (SE) is calculated using the formula sqrt{ p * ( 1 - p ) * [ (1/n1) + (1/n2) ] }, where n1 and n2 are the sizes of population 1 and 2 respectively. Substituting the values, we get SE = sqrt{ 0.0680 * ( 1 - 0.0680 ) * [ (1/510) + (1/460) ] } = 0.0161.
The test statistic (z) is calculated using the formula (p1 - p2) / SE. Substituting the values, we get z = (0.0745 - 0.0609) / 0.0161 = 0.842.
So, the correct value of the test statistic is z = 0.842. This means that the difference in the proportion of lost bags between the two airlines is 0.842 standard errors above the mean difference of 0. This suggests that Standard Air may have a higher population proportion of lost bags on international flights, but we would need to compare this test statistic to a critical value to make a definitive conclusion.
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