"Walking in the Airport, Part I Do people walk faster in the a...

Question

"Walking in the Airport, Part I Do people walk faster in the airport when they are departing (getting on a plane) or when they are arriving (getting off a plane)? Researcher Seth B. Young measured the walking speed of travelers in San Francisco International Airport and Cleveland Hopkins International Airport. His findings are summarized in the table.

b. Explain why it is reasonable to use Welch’s t-test.
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b. Explain why it is reasonable to use Welch’s t-test.

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Accepted Answer

Welcome back everyone. In this problem, a psychologist recorded reaction times in milliseconds for two independent groups participants after consuming a caffeinated drink and participants after consuming a placebo. The sample variances differ noticeably, and each group has about 30 subjects. Which test should the psychologists use to determine whether the mean reaction times differ between the groups? A says to use a 2 sample Z test because both sample sizes are around 30, so the Z test is always preferred. B says to use Welch's T test because the samples are independent. The variances appear unequal, and the sample sizes give approximate normality of means. C says to use a man-Whitney U test because the sample variances differ and that always prohibits mean-based tests. And the D says to use a chi square test for variance equality because the goal is to compare means. Now let's think about the information that we have to help us determine which test we should use. What do we already know? Well, for starters, we know that the psychologist recorded reaction times in milliseconds for two independent groups. So this tells us, OK, first of all, let me put this in a red here. That the data is quantitative because we're talking about times in milliseconds, OK. And it's from two independent groups. Right, that's the group for the the the that had the caffeinated drink and the group that consumed the placebo. Now what else do we know? Well, we're also told that each group has about 30 subjects, OK? So that means here that since N. It has about 30 subjects, so we could say that N is greater than or equal to 30, or no, N is approximately 30 rather. So since it has about 30 subjects, that means the sample size is about 30, and thus that means the central limit theorem applies, OK. Because remember the the central limit theorem tells us that for a sample size that's large enough, generally 30 or more, then our distribution will approximately follow a normal distribution. It gives an approximate normality of means. Now what else do we know? Well, we're also told that the sample variances differ noticeably, OK, so since the variances differ noticeably. Then that tells us that if our variance is sigma squared, sigma squared 1 is not going to be equal to sigma squared 2, which means that the assumption of equal variances may not hold. Now let's ask ourselves, given this information that we have, which test is best for our samples that are independent with unequal variances and with sample sizes that give approximate normality of means? Welch's tea test. Welch's tea test would be best for this comparison. Therefore, B is the correct answer. We should use Welch's T test because the samples are independent, the variances appear unequal, and the sample sizes give approximate normality of means. We can be sure that we're correct by looking at the remaining answer choices. For example, in answer choice A, it tells us to use a two sample Z test, but the population standard deviation is unknown, OK? In other words, we don't know sigma, so that requires a T test. So that's how we know A is incorrect. C says to use a man-Whitney U test, but this is a nonparametric test for medians or distributions. Welch's T test can handle unequal variances while still comparing means. Finally, in D, it tells us to use a chi squared test. But remember, the goal is to compare means, not to test for association or in this case test the equality of variances. Therefore, chi square test would not be best. That's how we can be sure that B is the correct answer. Thanks a lot for watching everyone. I hope this video helped.

Key Concepts

Welch’s t-test

Assumption of Unequal Variances

Independent Samples

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