A researcher measured the walking speed of travelers in San Francisco Internatio

Question

A researcher measured the walking speed of travelers in San Francisco International Airport and Cleveland Hopkins International Airport. The standard deviation speed of the 260 travelers who were departing was 53 feet per minute. The standard deviation speed of the 269 travelers who were arriving was 34 feet per minute. Assuming walking speed is normally distributed, does the evidence suggest the standard deviation walking speed is different between the two groups? Use = 0.05 level of significance.

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Explanation / Answer

Solution:-

Given,

The standard deviation speed of the 260 travelers (i.e., n1 = 260) who were departing was 53 feet per minute (Standard deviation, s1 = 53). The standard deviation speed of the 269 travelers (n2 = 269) who were arriving was 34 feet per minute (s2 = 34).

Assuming walking speed is normally distributed, does the evidence suggest the standard deviation walking speed is different between the two groups?

Use = 0.05 level of significance.

Given sample sizes of n1 and n2, the test statistic will have n11 and n21 degrees of freedom, and is given by the following formula.

If the larger variance (or standard deviation) is present in the first sample, then the test is right-tailed. Otherwise, the test is left-tailed. Most tables of the F-distribution assume right-tailed tests, but that requirement may not be necessary when using technology.

Here,

Assuming walking speed is normally distributed, lets work out to see if the evidence suggest the standard deviation of walking speed is different between the two groups

   = (53)2 / (34)2

= 2809 / 1156 = 2.4299

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