3. (HW8 Question 5) For a sports radio talk show, you are...

3. (HW8 Question 5) For a sports radio talk show, you are asked to research the question whether more home runs are hit by players in the National League or by players in the American League. You decide to use the home run leaders from each league for a 40-year period as your data. sample size sample mean sample variance National League 40 44.75 78.91 American League 40 42.88 61.19 At $\alpha = 0.05$, is there sufficient evidence to conclude that the National League hits more home runs than the American League? (a) State the null and alternative hypotheses. (b) Find a test statistic. (c) Find a rejection region. (d) Make the decision based on the rejection region.

Transcript

00:01 So we're looking at 50 players randomly chosen from the american league and we have in millions of dollars what the average mean and standard deviation is of those 50 players.

00:13 And for the national league we have 50 players with a mean and a standard deviation.

00:18 And we're told that our degrees of freedom is approximately 82.

00:23 And we want for number one, a statistically -minded baseball fan wants to use statistical inference to determine if the salaries of the players are different.

00:33 And so we will be assuming that the mean of the first group, the al, is equal to that of the second group versus the mean of the first group does not equal the mean of the second group.

00:48 So that will correspond with your letter b.

00:52 Next you want to calculate the appropriate test statistic.

00:57 And that test statistic, or question two, will end up being, since we don't know the population standard deviations, will be a t -value that will have about 82 degrees of freedom.

01:12 And we do find that by taking the difference between the two, which is that three point, i'm just going to write the formula, x -bar one minus x -bar two, and then we're going to divide it by that standard deviation squared, divided by the sample size, and the standard deviation of the second group squared divided by the sample size.

01:34 And i'm actually going to plot these, pop these into my calculator, and so let me go back to this data.

01:39 And so this is a, in stat and test, a two -sample t -test.

01:44 And x -bar one is at three point zero nine seven, and the standard deviation five point nine zero eight, and n one is 50.

01:56 X sub two is at four point six eight four, with a standard deviation of nine point four nine five.

02:04 Notice that both of them are larger than the mean, with a sample size of 50.

02:09 And we're going to have not equal to, i'm going to say no to pooling.

02:14 And when we calculate, we do end up getting that degrees of freedom that they say.

02:19 But our test statistic comes out to be that t -value.

02:23 And let's see, do you have a specified number of decimals? i don't see that...

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