A football coach is observing 15 football players during training camp. He is comparing the number of goals the players made during the pre-training and post-training games. They are testing to see if there is a significant difference in the player's game. Here since the same players are used to compare the results, we call it a dependent sample test.

HYPOTHESIS TEST

a. a brief statement of the purpose of the study.

The goal of the study is to test whether there is a significant difference on how the players perform before training and after training.

b. Define the populations (the population before and after).

X1=X1=Pre training

X2=X2=Post training

c. State the hypothesis for the study.

From the information given we set the hypothesis as

H0=H0=There is no significant difference between the players' games. 0=00=0

H1=H1=There is a significant difference in the players' games. 0000

d. Select a level of significance.

5% = 0.05

e. State how the sample was selected.

n=samplesize=15n=samplesize=15

f. Show the raw data in a table.

Sample	Pre-Training	Post-Training	Difference in pairs (D=X1-X2) = -19	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

g. Decide which statistical test is appropriate and compute the test statistic

(z or t). Why is the test appropriate? Find the critical value(s).

Based in the information received, the significance level is

=0.05=0.05 and the value the value of the T-Test gives usn1=14n1=14 degrees of freedom

tc=tc=Critical value = 2.145

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

differences in pairs, the test statistic.

I decided to use paired T-test

Two variables were given

X1=1= Pre training

X2=2= Post training

I decided to check if there is a significant difference in how the players perform before and after training\

t=DDSDnt=DDSDn wheren=samplen=sample ,Di=X1X2Di=X1X2,D=MeanD=Mean,SD=SD=Standard deviation

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

at football or has not changed/improved a person's proficiency.

at football.

There is enough evidence to claim that a major difference is seen in players' performance.

k. Summarize the results.

It has been concluded that the null hypothesis

(H0)H0 is rejected.

CONFIDENCE INTERVAL ESTIMATION

a. Construct a confidence interval. Show the computations,

b. Select a level of significance.

c. Find the critical value(s).

d. State the conclusion

e. Summarize the results.