Question

1. You want to see if students from different types of schools are equally (or unequally) happy. You randomly sample groups of 10 students from three different sizes of school and have them fill out a standardized scale measuring satisfaction with their education. This scale has a potential range from 0-50 (larger scores = greater satisfaction).

Small       Schools	Rank	Medium Schools	Rank	Large Schools	Rank
17	5.5	13	2	35	29
21	11	20	9	26	22
14	3	30	26	17	5.5
24	19	24	19	21	11
18	7	27	23	34	28
22	14	29	24.5	22	14
19	8	31	27	29	24.5
22	14	24	19	41	30
11	1	25	21	23	16.5
23	16.5	16	4	21	11

     

       ΣX =191      Σrank = 99    ΣX = 239      Σrank = 174.5    ΣX = 269    Σrank = 191.5

       ΣX² = 3805                           ΣX² = 6033                               ΣX² = 7763

        SS = 156.9                          SS = 320.9                                 SS = 526.9          

You have conducted an experiment to see if the type of chairs placed in a lecture hall affect attendance. You divide your lecture rooms into 3 groups and put one type of chair in each room. You then record the average number students absent each day for an entire term.

Source             SS        df         MS      F                                                                 Type of Chair

Between          520      2          260      6.34                                                      plastic        cloth   leather

Within             492      12        41                       Mean # of students/lecture       42             28           32

Total                1012    14

b) After collecting the data you are curious to see if plastic and leather groups differ. If you want to use a powerful test, what do you find?    

Answer 1

a) We want to understand if the satisfaction level between 3 types of school are same. We define average satisfaction level in three different types of schools as

The Hypothesis we want to test

against

From the given table we construct the ANOVA

SUMMARY
Groups	Count	Sum	Average	Variance
Small School	10	191	19.1	17.43333
Medium Schools	10	239	23.9	35.65556
Large Schools	10	269	26.9	58.54444
ANOVA
Source of Variation	SS	df	MS	F Observed	P-value	F crit
Between Schools	309.6	2	154.8	4.160048	0.026614	3.354131
Within Schools	1004.7	27	37.21111
Total	1314.3	29

Since F Observed is > F Critical, we reject the Null Hypothesis and conclude that the students in different types of achool are not equally happy

b) Here we want to check the following Hypothesie

H₀: There is no effect of attendance on the basis of chair

against

H₁: There is effect on attendance on the basis of chair

The F Observed Value is 6.34

F critical value with 2,12 df at 5% is 3.89

Since F Observed > F Critical , we reject the Null Hypothesis and conclude, chair plays a critical role with attendance