Consumer Research reported information on the time required for caffeine from pr

Question

Consumer Research reported information on the time required for caffeine from products such as coffee and soft drinks to leave the body after consumption. Suppose that the 95% confidence interval estimate for the population mean time for adults from 5.6 hours to 6.4 hours. a. What is the point estimate of the mean time for caffeine to leave the body of adults after consumption? b. If the population standard deviation was known to be 2 hours, approximately how large a sample was used to obtain this confidence interval?

Explanation / Answer

We know that the confidence interval at 95% confidence is given as (5.6,6.4)

a) Point estimate for mean will be (5.6+6.4)/2=6

b) We know that for 95% confidence, z value is 1.96. Thus, 6.4=6+(1.96*2)/sqrt(n)

this gives sqrt(n)=9.8 or n is 96.04 or 97

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