A lab is testing the amount of a certain active chemical com

A lab is testing the amount of a certain active chemical compound in a particular drug that has been recently developed. The manufacturer claims that the average amount of the chemical is 90 mg. It is known that the standard deviation in the amount of the chemical is 7 mg.

A random sample of 34 batches of the new drug is tested and found to have a sample mean concentration of 93.8 mg of the active chemical.

You may find this standard normal table useful throughout the following questions.

a)Calculate the 90% confidence interval for the mean amount of the active chemical in the drug. Give your answers to 2 decimal places.

                ? ? ?         

b)At a significance level ? = 0.1, the null hypothesis that the population mean amount of the active chemical in the drug is 90 mg is rejected or not regected

Solution

(a)Given a=1-0.9=0.1, Z(0.05) = 1.645 (from standard normal table)

So the lower bound is

xbar - Z*s/vn=93.8 -1.645*7/sqrt(34)=91.83

So the upper bound is

xbar + Z*s/vn =93.8 +1.645*7/sqrt(34) =95.77

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(b) Since the interval in part a is not include 90, we reject the null hypothesis.