Two pain relief drugs are being considered. Drug 1 has shown in the past to have
ID: 3153958 • Letter: T
Question
Two pain relief drugs are being considered. Drug 1 has shown in the past to have a standard deviation 1 = 4 minutes. A random sample of 8 doses of the first drug showed that the average amount of time required before the drug was absorbed into the bloodstream was (x_1 ) = 24 minutes. For the second drug, the historical data indicated a standard deviation 2 = 3.9 minutes. A random sample of 10 doses showed the average time required for absorption was (x_2 ) = 29 minutes. Assume the absorption times follow a normal distribution. a. Should you use the Z-Distribution or T-Dstribution in determining a confidence interval in this problem? Explain. b. Find a 95% confidence interval for the difference in average absorption time for the two drugs. c. Does it appear that one drug is absorbed faster than the other (at the 95% level)? Explain.
Explanation / Answer
a)
We use z distribution becasue we know the population standard deviations and the original distributions are normal already.
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b)
Calculating the means of each group,
X1 = 24
X2 = 29
Calculating the standard deviations of each group,
s1 = 4
s2 = 3.9
Thus, the standard error of their difference is, by using sD = sqrt(s1^2/n1 + s2^2/n2):
n1 = sample size of group 1 = 8
n2 = sample size of group 2 = 10
Also, sD = 1.876432786
For the 0.95 confidence level, then
alpha/2 = (1 - confidence level)/2 = 0.025
z(alpha/2) = 1.959963985
lower bound = [X1 - X2] - z(alpha/2) * sD = -8.67774068
upper bound = [X1 - X2] + z(alpha/2) * sD = -1.32225932
Thus, the confidence interval is
( -8.67774068 , -1.32225932 ) [ANSWER]
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c)
Yes, because the whole interval is totally less than 0. [ANSWER]
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