Question

10. The test taking times (in minutes) for Algebra students from my morning, afternoon and evening classes are listed below. Use a 0.05 significance level to test the claim that the different classes have the same test taking time.

Morning Class 24   21   23   30   23

Afternoon Class 25   31   23   20   28

Evening Class 23   27   22   30   20

USE A 0.05 SIGNIFICANCE LEVEL TO TEST THE CLAIM:

H0: All the means are the same. (generic null hypothesis)

H1:At least one mean is different. (generic alternative hypothesis)

Test Statistic: F=_________ Q37(ROUND TO 3 DECIMAL PLACES)

P-value: p=___________Q38(ROUND TO 4 DECIMAL PLACESzero place holders)

Decision/Conclusion: _________________________________Q39(CIRCLE ONE BELOW) Reject H0, There is sufficient evidence to warrant the rejection of the claim that the means are the same.

OR

Fail to Reject H0, There is not sufficient evidence to warrant the rejection of the claim that the means are the same.

Answer 1

	Morning	Afternoon	Evening	Total
1	24	25	23
2	21	31	27
3	23	23	22
4	30	20	30
5	23	28	20
Total	121	127	122	370
Mean	24.2	25.4	24.4
Squares	2975	3299	3042	9316

This is ANOVA - Single Factor. We first need to find the and . They are 'Total variance' and 'Variance in between the treatments' respectively.

We know

=

Grand total = 370 Sum of individual squares = 9316

= 189.333

=

Note: We have to separately sum for all the treatment.

=

= 9130.8

= 4.1333

Df (Bet) = k -1 ………..where k = no. of treatments

= 2

189.333 - 4.133

= 185.2

Df (res) = n – k

=15 - 3

= 12

ANOVA
Source of Variation	SS	df	MS  (SS /df)	F
Between Groups	4.1333	2	2.0667	0.1339
Within Groups	185.2000	12	15.4333
Total	189.3333	14

H0: All the mean test time for all the class are the same.

H1:At least one mean test time is different.

Test Stat = F-ratio

= MSB / MSW

= 2.0667/ 15.4333

Test Statistic: F=_0.1339_

p-value = P( > F-stat)

= P( > 0.13) ......................using f-dist with df1 = 2, df2 = 12

P-value: p=_0.8760_Q38(ROUND TO 4 DECIMAL PLACESzero place holders)

Since p-value > 0.05

Decision/Conclusion:

Fail to Reject H0, There is not sufficient evidence to warrant the rejection of the claim that the means are the same.

p-value is the probability that the null hypothesis is true by chance.