Question

3. Twelve different students were randomly selected and tested on Friday and Mon day. The table below shows results for each student. Monday s Table 3 Exam Results Sd: 5.2 points) Construct a confidence interval for the mean of all differences p 374422.1 At a = 0.1 lev ificance, test the claim that the giving exams on Mon- days help mcreasine exam results by using the data in table 3. (b) (3 points),lear state Ho H, identify the claim and type of test (e) (3 points) Find all related critical values, draw the distribution, clearly mark and shade the critical region(s). Drawing& Shading Required. NcR (d) (2 points) Find the computed test statistic and the P-value. tTest C.T.S. P-Value : - (e) (2 points) Use non-statistical terminology to state your final conclusion about the claim CTSs Ho: Page 4 of 4 Study Guide 31 Total Points: 50

Answer 1

The following table is obtained:

	Friday	Monday	Difference = Friday - Monday
	75	80	-5
	83	80	3
	78	75	3
	93	88	5
	65	65	0
	75	73	2
	90	91	-1
	80	85	-5
	100	95	5
	81	93	-12
	68	72	-4
	90	86	4
Average	81.5	81.917	-0.417
St. Dev.	10.335	9.337	5.195
n	12	12	12

For the score difference

Mean, $\bar x_d$ = -0.417

Sample standard deviation, $s_d$ = 5.195

$\alpha$ = 0.1

a) At $\alpha$ = 0.1 amd df = 12-1 =11, critical value, _{$t_{\alpha/2}$}= 1.796

90% confidence interval for the mean of all differences

$\left (\bar x_d -t_{\alpha /2}*\frac{s}{\sqrt{n}}, \ \bar x_d +t_{\alpha /2}*\frac{s}{\sqrt{n}} \right )$

$\left (-0.417 -1.796*\frac{5.195}{\sqrt{12}}, \ -0.417+1.796*\frac{5.195}{\sqrt{12}} \right )$

$(\textbf{-3.110, 2.276})$

b) Given the exams on Monday helps increasing exam result mean: Friday - Monday < 0

Null and Alternative Hypotheses

$H_o: \mu_D\geq 0$

$H_1: \mu_D< 0$

This corresponds to a left-tailed test, for which a t-test for two paired samples be used.

c) One tailed critical value, t_c = −1.363

d) Test Statistics

$t = \frac{\bar x_d}{s_d/ \sqrt n} = \frac{ -0.417}{ 5.195/ \sqrt 12} =\textbf{ -0.278}$

P-value = 0.6068

e) Conclusion

As P= 0.6068 > 0.1 we fail to reject the null hypothesis.

There is not enough evidence to claim that Monday helps increasing exam results​, at the 0.1 significance level.