The us department of transportation provides the number of...

The U.S. Department of Transportation provides the number of miles that residents of the 75 largest metropolitan areas travel per day in a car. Suppose that for a random sample of 72 Buffalo residents the mean is 20.4 miles a day . The standard deviation of the population (Buffalo residents) is 8.2 miles a day. For an independent random sample of 54 Boston residents the mean is 16.4 miles a day. The standard deviation of the population (Boston residents) is 7.6 miles a day. At 90% confidence, what is the absolute value of the margin of error ?

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Transcript

00:01 In this problem, we're given the following information.

00:02 The sample mean for our first population is 22 .5.

00:07 The sample mean for our second population is 18 .6.

00:11 The sample standard deviation for our first population is 8 .4.

00:16 The sample standard deviation for our second population is 7 .4.

00:20 The sample size of our first population is 50.

00:23 The sample size of our second population is 40.

00:25 So the first thing the question asks us to do is find a point out.

00:30 Estimate for the difference of population means and that is x bar 1 minus x bar 2 which is equal to 22 .5, let me do this in a different color, 22 .5 minus 18 .6 which is equal to 3 .9.

00:51 Oh, that does not say 3 .9.

00:56 So this is our point estimate.

01:02 And in part b, we are asked to find a confidence interval, a 95 % confidence interval.

01:12 So in order to find a confidence interval, we need the following information.

01:17 The t statistic of alpha over 2, and for us, our alpha is equal to 1 minus our confidence level, which is 0 .95.

01:27 So this is 0 .05.

01:29 So for us, we need a t statistic at 0 .025.

01:35 And we also need to compute, for our t test statistic, a degrees of freedom.

01:41 So what is our degrees of freedom? let's first compute that...

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