Question

Please answer part a) through part f) of the question below. Thank you.

Question 2

Administrators at ACME High School wanted to know which of four
instructional methods for mathematics is best. The four methods were
lecture only (L), lectures with remedial textbook assistance (LR),
lectures with computer assistance (LC), and computer instruction only
(C). At the end of five weeks, the students were given a common
exam. The scores on the exams are below.

Student	L	L/R	L/C	C
1	7	5	9	17
2	2	2	12	19
3	2	3	2	26
4	6	11	17	1
5	16	16	12	47
6	11	11	20	27
7	9	3	20	-8
8	0	N/A	31	10
9	4	N/A	21	20
10	2	N/A	N/A	N/A

a) Which instructional method results in the highest median score
gain?

b) Which method results in the highest mean score gain?

c) Which method has the smallest coefficient of variation?

d) Which method has the largest sample standard deviation?

e) Which test (Hartley’s F-max, Bartlett’s, Levene’s) is most
appropriate for checking for equality of variance?

f) Run the test you suggested in part (e). Be sure to state the null
and alternative hypotheses, test statistics, p-value, and
conclusion. Also, check the assumptions with graphs, Anderson-
Darling, etc.

Answer 1

Statistics Summary

Statistic	L	L/R	L/C	C
a) Median	5	5	17	19
b) Mean	5.9	7.29	16.0	17.67
c) CV %	84.4	73.8	52.3	89.9
d) s	4.98	5.38	8.37	15.89

a) C-Method gives highest Median Score

b) C-Method gives highest Mean Score

c) L/C-Method gives smallest CV%

d) C-Method gives largest sample standard deviation

e) Following Probability Graph by Anderson-Darling Test shows that all instructional methods of mathematics fits for normal distribution with each of method's p-value >0.05.Since all data are coming from normal distribution,Levene test can be applied and appropriate here

f) The null and alternate hypothesis for testing equality and non-equality of variance are given below

Ho: => all instructional methods are having equal variance

A12 = 2 = 3 = 04

Ha: for at least one pair (i,j) =>at least one pair of instructional methods are not equal

oi toj

Minitab output of Levene's test gives the p-value as 0.092 which is > 0.05 that is we fail to reject Ho meaning that equality of variance is prevalent among all instructional methods of mathematics

Probability Plot of L, L/R, L/C, C Do X Probability Plot of L, L/R, L/C, C Normal - 95% CI Variable EL/R - LIC - Percent Mean StDev NADP 5.9 4.977 10 0.355 0.383 7.286 5.376 7 0.474 0.160 16 8.367 90.237 0.701 17.67 15.89 9 0.230 0.726 - --- -25 50 75 25 Data

Multiple Comparisons P-Value 0.067 Levene's Test P-Value 0.092