Question

Choose a variable that will allow the use of dependent samples. For example, you might wish to see if a persons’ proficiency at softball has changed/improved after a training camp. Do not use variables that are presented in the course in order to illustrate the concept. Select a sample of data (10 to 20) value pairs (e.g. before and after), and then complete the following:

i. Show the computations of the sample statistic, the standard deviation of the

   differences in pairs, the test statistic.

j. State the decision. A training camp has changed/improved a person’s proficiency.

   at softball, or has not changed/improved a person’s proficiency.

   at softball.

k. Summarize the results.

l. Construct a confidence interval. State the conclusion. Summarize the results.

Answer 1

We can use football training sample test where the number of goals the players made in the pre-training and in the post-training games. Then their comparison can be made. Here since the same players are used to compare the results we call it a dependent sample test.

Sr.	Pre	Post	D  (Pre - post)	D^2
1	5	7	-2	4
2	7	9	-2	4
3	10	11	-1	1
4	7	8	-1	1
5	5	6	-1	1
6	8	8	0	0
7	7	6	1	1
8	10	9	1	1
9	9	10	-1	1
10	8	12	-4	16
11	8	11	-3	9
12	5	8	-3	9
13	5	6	-1	1
14	5	8	-3	9
15	7	6	1	1
Total			-19	59
Mean			-1.267
SD			1.580

Mean =

SD =

Test

(There is no difference between number of goals in pre and post training )

(There are more number of goals after the training than before.)

Since we have d = pre - post are favourable would be -d

Test Stat =

= .......where null difference = 0

Test Stat : -3.1057

Taking level of significance = 0.05

Since this is a one tailed test

Critical value =

=

= 2.1448

Since |Test Stat| > C.V.

We reject the null hypothesis at 0.05 and conclude that training significantly improved the players game play.

(1 - )% confidence interval for the mean difference

Again taking the level of significance = 0.05