Question

2. A training program was created in order to improve performance in a sit-and-reach exercise done in fitness. The creators claim that those who enroll in the program will find their distance increased. A random sample of 12 people enrolled in the training was selected. A measure of each person's distance was recorded before the start of and just after completion of the program. The data are shown in the table below. Person | Before Program | After Program A | 6.7 | 7.8 B | 5.4 | 5.9 C | 7.0 | 7.4 D | 6.6 | 6.6 E | 6.9 | 7.6 F | 7.2 | 7.7 G | 5.5 | 6.2 H | 7.1 | 7.0 I | 7.9 | 7.8 J | 5.9 | 6.4 K | 8.4 | 8.7 L | 6.5 | 6.5 Total | 81.1 | 85.6 Do the data provide statistically compelling evidence of an increase in the average distance obtained after completion of the program? Justify your decision with the appropriate statistical procedures.

          2. A training program was created in order to improve performance in a sit-and-reach exercise done in fitness. The creators claim that those who enroll in the program will find their distance increased. A random sample of 12 people enrolled in the training was selected. A measure of each person's distance was recorded before the start of and just after completion of the program. The data are shown in the table below.

Person | Before Program | After Program
A | 6.7 | 7.8
B | 5.4 | 5.9
C | 7.0 | 7.4
D | 6.6 | 6.6
E | 6.9 | 7.6
F | 7.2 | 7.7
G | 5.5 | 6.2
H | 7.1 | 7.0
I | 7.9 | 7.8
J | 5.9 | 6.4
K | 8.4 | 8.7
L | 6.5 | 6.5
Total | 81.1 | 85.6

Do the data provide statistically compelling evidence of an increase in the average distance obtained after completion of the program? Justify your decision with the appropriate statistical procedures.

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2. A training program was created in order to improve performance in a sit-and-reach exercise done in fitness. The creators claim that those who enroll in the program will find their distance increased. A random sample of 12 people enrolled in the training was selected. A measure of each person's distance was recorded before the start of and just after completion of the program. The data are shown in the table below.

Person | Before Program | After Program
A | 6.7 | 7.8
B | 5.4 | 5.9
C | 7.0 | 7.4
D | 6.6 | 6.6
E | 6.9 | 7.6
F | 7.2 | 7.7
G | 5.5 | 6.2
H | 7.1 | 7.0
I | 7.9 | 7.8
J | 5.9 | 6.4
K | 8.4 | 8.7
L | 6.5 | 6.5
Total | 81.1 | 85.6

Do the data provide statistically compelling evidence of an increase in the average distance obtained after completion of the program? Justify your decision with the appropriate statistical procedures.

Added by Lisa S.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

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Solved by Expert Lynn Larson

09/15/2023

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First, we need to find the differences in distances for each person before and after the program. Show more…

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A training program was created in order to improve performance in a sit-and-reach exercise done in fitness. The creators claim that those who enroll in the program will find their distance increased. A random sample of 12 people enrolled in the training was selected. A measure of each person's distance was recorded before the start of and just after completion of the program. The data are shown in the table below.

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Transcript

00:01 So we're talking about doing a matched pair, one sample t -test here.

00:05 We have a before and after table with the 12 people in the table.

00:09 And so what i did over here on the right side is i subtracted the after minus the before, because we want more positive answers than negative answers.

00:22 So i did the differences here.

00:26 And so you end up getting mostly positive answers here.

00:28 The first one, you end up with a 1 .1, 7 .8 minus 6 .7.

00:33 And then you get a 0 .5, 5 .9, et cetera, 7 .4 minus 7 .0.

00:40 And what i did was i found the mean and standard deviation for this new list.

00:46 The new list, the mean is 0 .375, and the standard deviation is 0 .372.

00:53 So i take that information now and do a hypothesis test for a matched pair.

00:57 So whenever we do a matched pair, our ho always starts out as mu equals 0, because the null is that there is no difference.

01:09 So the hypothesis would be that mu equals 0.

01:11 The difference between them is 0.

01:13 You can see on the table that there's a couple of them that are 0.

01:16 There's a couple that are negative, and lots of them are positive.

01:18 So we'll see what happens.

01:19 And then we're trying to test if this program helped or improved score or reach.

01:24 So we're going with a greater than 0 there.

01:26 So it's a one -tailed test.

01:27 We're trying to find that p -value over there.

01:31 The test statistic formula, x bar minus the mean over the standard deviation over the square root of n, the degrees of freedom is going to be 11, because i have 12 in my sample.

01:41 So it's just a matter of plugging in the values that i've figured out...

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