Question

1. An investigator wishes to compare the average time to relief of headache pain under three distinct medications, call them Drugs A, B, and C. Fifteen patients who suffer from chronic headaches are randomly selected for the investigation, and five subjects are randomly assigned to each treatment. The following data reflect times to relief (in minutes) after taking the assigned drug. Test if there is a significant difference in the mean times among three treatments

Drug A	Drug B	Drug C
30	25	15
35	21	20
40	30	25
25	25	22
35	30	24

State the null and alternative hypothesis.

-Null: all means are equal

-Alternative: at least one mean is different

b) State your conclusion about the hypothesis based on the test statistic and critical value

Answer 1

For the given data using Anova single factor in Excel we get output as

ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	350.8	2	175.4	8.36566	0.005308	3.885294
Within Groups	251.6	12	20.96667
Total	602.4	14

so from the above output

( b )

Test statistic = 8.37

Assuming alpha = 0.05 ,

df = ( 2,12 )

F critical value = 3.89

Decision :

F CAL < F CRIT

i.e., 8.37 >  3.89

so reject the null hypothesis

conclusion  

At alpha = 0.05 l.o.s   there is a significant difference in the mean times among three treatments