A sample of 30 commuters in the area of a certain city...

A sample of 30 commuters in the area of a certain city yielded the accompanying commute times, in minutes. Preliminary data analyses indicate that the t-interval procedure can reasonably be applied. Find and interpret a 90 % confidence interval for the mean commute time of all commuters in the area of the city. (Note: x overbar equals25.63 minutes and s equals9.29 minutes.)

Transcript

00:01 So in this question, we are assuming 30, in this case here, we have 30 observations, a sample of 30 observations.

00:11 And from this, we have that the sample mean is equal to 25 .63 minutes.

00:17 And that the sample standard deviation is equal to 929 minutes.

00:22 So consider these information, the question is saying that we can compute the t interval.

00:30 So the procedure is reasonably applied.

00:35 So the only thing that we need to do is know what is the formula to compute a t interval for the mean, because we are interested in the mean.

00:44 So the first thing that we need to know is the confidence level.

00:48 So we are assuming 95 % of confidence level here, which means that in the formula here we have x bar plus and minus the since you are working with a t interval, this is a little t that i'm going to explain how can we obtain this.

01:08 Multiply by this s divided by the square root of n.

01:12 This little t depends on this value here.

01:16 So t here is the value or the quantile in the t student distribution with degrees of freedom equals to n minus 1.

01:27 So in our case, the degrees of freedom is 29.

01:31 Because we want to have a 90 % confidence interval, this means that the area left to this number that we want is equal to 0 .90, 0 .9, which is the proportion related to this percentage, plus half of what is left of this.

01:51 So if i have 90%, i have 10 % left...

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