Question

A pharmaceutical manufacturer has been researching new medications formulas to provide quicker relief of arthritis pain. Their laboratories have produced three different medications and they want to determine if the different medications produce different responses. Fifteen people who complained of arthritis pains were recruited for an experiment; five were randomly assigned to each medication. Each person was asked to take the medicine and report the length of time until some relief was felt (minutes). The results are shown below. (Assume normal distributions with equal variances.)

Med. 1 Med. 2 Med. 3

4 2 6

8 5 7

6 3 7

9 7 8

8 1 6

1. Set up the ANOVA Table. Use a=0.05 to determine the critical value.

2. Do these data provide sufficient evidence to indicate that differences in the average time of relief among three medicines? Use a=0.05

Answer 1

Null hypothesis ( H0) :there is no differences in the average time of relief among three medicines

i.e.,

Alternative hypothesis ( Ha ) : there is differences in the average time of relief among three medicines

( 1 ) Using Anova single factor in Excel we get output as :

Anova: Single Factor
SUMMARY
Groups	Count	Sum	Average	Variance
Med 1	5	35	7	4
Med 2	5	18	3.6	5.8
Med 3	5	34	6.8	0.7
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	36.4	2	18.2	5.2	0.023637	3.885294
Within Groups	42	12	3.5
Total	78.4	14

( b ) From the above table

F cal > F critical

i.e ., 5.2 > 3.89

so reject the null hypothesis

Conclusion :

at a = 0.05 l.o.s there is sufficient evidence to indicate that differences in the average time of relief among three medicines