Testing the Difference Between Two Means (c) calculate d̄ and ...

Question

Testing the Difference Between Two Means (c) calculate d̄ and Sd, Assume the samples are random and dependent, and the populations are normally distributed.

[APPLET] Passing Play Percentages The passing play percentages of 10 randomly selected NCAA Division 1A college football teams for home and away games in the 2020–2021 season are shown in the table. At , α=0.20 is there enough evidence to support the claim that passing play percentage is different for home and away games? (Source: TeamRankings)

Table displaying home and away passing play percentages for 10 NCAA Division 1A college football teams.

Accepted Answer

All right. Hello, hello, everyone. So, this question says, the number of correct quiz answers by 5 students before and after a study technique is given below. Find the mean and standard deviation of the differences before subtracted by after. Here we have 4 different answer choices labeled A through D. So here on the right side of the screen, I went ahead and just rewrote the data that we're already given, that is the scores before and after for all 5 students. So first, let's find the differences, that is the before subtracted by the after. So here, in the table that I've written on the right side, we can go ahead and subtract the values in each row. For example, 12. Subtracted by 13. Equals -1 14 subtracted by 16 equals -2. 13 subtracted by 14 equals -1. 11 subtracted by 12, and also 15 subtracted by 16, both equal -1 as well. So now, these are your differences. Or D So now we can find the mean of these differences. Which essentially is equal to the sum of all differences, all individual differences divided by n. Ultimately, D is equal to. -6 subtracted by 5. Which equals -1.2. And now you can find the standard deviation of these differences. Now, because this is a sample, you would use the formula for the sample standard deviation. So S is equal to the square root of. The sum Of all square differences between D and D bar. Divided by and subtracted by one. So let's go through this formula. The numerator. You would find as follows. Recall that earlier, you calculated a value for D for each row of the data, right? So what you do now is you take each value of D and you subtract D bar, which is the mean of the differences. So for example, You would calculate -1. Subtracted by -1.2. And then you would take this difference and you would square it. To give you A different number, which in this case is 0.04. And then you would repeat this calculation for the remaining 4 values and find the sum of all of them. So ultimately, The sum of square deviations. Is equal to 0.80. To the square root of 0.80. Subtracted by, or excuse me, divided by 5 subtracted by 1, gives you a value of S equal to 0.20. Or actually, let me correct myself. 0.20 is actually the number inside of the square root after you you evaluate that expression. So S is equal to the square root of 0.20. Which equals approximately 0.447. And there you have it. So, D bar is equal to -1.2, and S is equal to 0.447. Which corresponds to option D in the multiple choice. And so with that being said, thank you so very much for watching, and I hope you found this helpful.

Key Concepts

Dependent Samples

Difference of Means

Hypothesis Testing

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