A paper investigated the driving behavior of teenagers by...

A paper investigated the driving behavior of teenagers by observing their vehicles as they left a high school parking lot and then again at a site approximately 1/2 mile from the school. Assume that it is reasonable to regard the teen drivers in this study as representative of the population of teen drivers. Amount by Which Speed Limit Was Exceeded Male Driver Female Driver 1.3 -0.2 1.3 0.5 0.9 1.1 2.1 0.7 0.7 1.1 1.3 1.2 3 0.1 1.3 0.9 0.6 0.5 2.1 0.5 (a) Use a .01 level of significance for any hypothesis tests. Data consistent with summary quantities appearing in the paper are given in the table. The measurements represent the difference between the observed vehicle speed and the posted speed limit (in miles per hour) for a sample of male teenage drivers and a sample of female teenage drivers. (Use ?males - ?females. Round your test statistic to two decimal places. Round your degrees of freedom down to the nearest whole number. Round your p-value to three decimal places.) t = df = P =

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00:04 We are looking at the driving behavior of teenagers observed as they left the high school parking lot and then again at a site approximately one half mile from the school.

00:18 And we want to test whether there's a difference in this behavior.

00:22 So these values are for the males and females, respectively.

00:27 And this is the amount by which speed limit was exceeded.

00:31 So if the speed limit was 25, for example, this person was 1 .3.

00:35 Miles above miles per hour above it whereas this person was driving below it by 0 .2 miles power.

00:43 All right.

00:43 So the null hypothesis is that the mean of these groups, so the mean of the males is equal to the mean of the females, the alternative hypothesis, because we're looking for, we're not told to go one direction, the males or females is squared than the other.

00:59 We'll just say not equal to.

01:00 So mu of males is not equal to mu of females.

01:08 And we're testing this at the alpha of 0 .01 level of significance.

01:13 And we're going to use the independent samples t test, and we're going to claim unequal variances.

01:23 So the unequal variances independent samples t tests.

01:47 So to do that, we're going to use this formula.

01:50 It's going to be the sample mean, of the males minus the sample mean of the females all over the square root of the sample variance of the males divided by the sample size of the males plus the sample variance of the females divided by the sample size of the female.

02:18 All right.

02:19 So let's go ahead and get this.

02:21 So i use my spreadsheet to do the calculations for us.

02:24 So here are the means and standard deviations for the males females here and these sample standard deviations.

02:31 I use the average functions.

02:33 So it equals average.

02:37 And this is in google sheets, but excel has a very similar formula.

02:42 And you put in the x values, the list here.

02:44 Sample standard deviation, st -d -e -v .s.

02:50 Put in the list to get your variables there.

02:52 Let me get your output there.

02:53 And that's that.

02:56 And then we square those values to get the variances.

03:04 More importantly for our work here, we need to get the degrees of freedom.

03:08 And when you have in unequal variances, independent samples t test, you calculate the degrees of freedom with this formula.

03:14 And so as a little, little shortcut, instead of having to input all these values, i make a separate variable in my spreadsheet for s squared over n because we're using that a bunch here...

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