Please show all work. An experiment was planned to assess if Vitamin C really do

Question

Please show all work.

An experiment was planned to assess if Vitamin C really does help cure the common cold more quickly. A random sample of 70 adults were randomized to one of two treatment groups. At the onset of a cold, subjects assigned to Group 1 received a placebo dose of vitamin C while subjects assigned to Group 2 received a daily dose of 4 mg of vitamin C. The treatment started on the day when the cold was first acknowledged by each person (onset) and continued until the cold symptoms were resolved. The response recorded for each subject was recovery time, measured in the number of days between onset and resolution. The researchers set the significance level to 5%.

Explanation / Answer

difference of mean=d=6.9-5.8=1.1

unpooled standard error of difference of means=SE(d)=sqrt(s12/n1 + s22/n2)=0.5704

t=d/SE(d)=1.1/0.5704=1.93

estimate df=(s12/n1 + s22/n2)/D and D=(s12/n1)2/(n1-1)+ (s22/n2)2/(n2-1)

estimated df=0.325333/0.002775=117.22 (next whole number is 118)

critical t(.05,118)=1.98

calculated t=1.93 is less than critical t=1.98 ,so we accept difference of the mean are statisticaly insignificant and null hypothesis is true

placebo 4mg Vit C n 30 32 mean 6.9 5.8 s 2.9 1.2 s2 8.41 1.44 s2/n 0.280333 0.045

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