Twentytwo volunteers at a cold research institute caught a c

Twenty-two volunteers at a cold research institute caught a cold after having been exposed to various cold viruses. A random sample of 10 of these volunteers was given tablets containing 1 gram of VItamin C four times a day. The control group, consiting of the remaining 12 volunteers, was given a placebo tablets that look the same as the Vitamin C tablets. The length of time the cold lasted was recorded.

Using the p value method, test if Vitamin C reduces the average time to recovery.

Solution

H0: mean average recovery time for vaitamin C= mean average recovery time for placebo

H1: mean average recovery time for vaitamin C< mean average recovery time for placebo

pooled standatd deviation=sqrt((9*0.672^2+11*0.882^2)/20)=0.830

test statistics=(6.45-7.125)/(0.830sqrt(1/10+1/12)=-1.899

p value=0.03605

as p value is less than 0.05 we can reject null hypothesis

so mean average recovery time for vaitamin C< mean average recovery time for placebo

so Vitamin C reduces the average time to recovery.