Question

The coach of the Dracut Marmosets, another soccer team, wants to determine if a stretching routine leads to a greater kicking performance for her team. Below are the distances (in meter) that a random sample of six players were able to kick a soccer ball before and after stretching. Assume that kicking distances are normally distributed. Use a =.05 los. (3 pts each) Player Player Player Player Player Player A B с D E F 74 47 73 68 70 57 Before Stretching After Stretching 83 54 75 72 82 69 1. State the null and alternate hypothesis: 2. Name the Test: 3. Determine the P-value: (Round to 4 places or 2 nonzero places). 4. Determine whether to Reject Ho or Fail to Reject Ho, and TELL WHY by relating P-value to a: 5. Interpret the result in a complete sentence with wording related to the problem:

Answer 1

1)

Let $x_1$ be Before stretching and be After stretching.

12

Here we have to test that

Null hypothesis:

HO: Ud=0

Alternative hypothesis:

0 > Prl: H

where $\mu_d=\mu_1-\mu_2$

2)

Paired t test

3)

Sample mean for difference (d):

$\bar{d}=\frac{\sum d}{n}=\frac{46}{6}=7.67$ (Round to 2 decimal)

$x_1$	12	di = C2 – 11	$(d_i-\bar{d})^2$ $=(d_i-7.67)^2$
74	83	9	1.769
47	54	7	0.449
73	75	2	32.149
68	72	4	13.469
70	82	12	18.749
57	69	12	18.749
		$\sum d=46$	$\sum (d_i-\bar{d})^2=85.333$

Sample standard deviation for difference (d) :

$s_d=\sqrt{\frac{\sum (d_i-\bar{d})^2}{n-1}}$

$s_d=\sqrt{\frac{85.333}{6-1}}$

$s_d=\sqrt{\frac{85.333}{5}}$

$s_d=\sqrt{17.06668}$

$s_d=4.131$ (Round to 3 decimal)

Test statistic:

$t=\frac{\bar{d}-\mu_d}{s_d/\sqrt{n}}$

$t=\frac{4.67-0}{4.131/\sqrt{6}}$

$t=\frac{4.67}{1.686474}$

t = 2.769 (Round to 3 decimal)

Test is left tailed test.

Degrees of freedom = n - 1 = 6 - 1 = 5

Level of significance = $\alpha$ = 0.05

P value from excel using function:

=T.DIST.(2.769,5,TRUE)

=0.9803 (Round to 4 decimal)

P value = 0.9803

4)
Here p value > $\alpha$

So we reject H0.

5)
Conclusion: There is sufficient evidence to determine that the stretching routine leads a greater kicking performance for her team.