Question

A new drug is introduced that is supposed to reduce fevers. Tests are done with the drug. The drug is given to 40 people who have fevers. It is found that the mean time that it takes for the fever to get back to normal for this test group is 320 minutes with a standard deviation of 60 minutes. Find the 90% confidence interval for the mean time that the drug will take to reduce all fevers for all people.

Answer 1

The 90% confidence interval for the mean time that the drug will take to reduce all fevers for all people is between 304 minutes and 336 minutes

Explanation:

We have the standard deviation for the sample, so we use the t-distribution to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 40 - 1 = 39

90% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 39 degrees of freedom(y-axis) and a confidence level of
`1 - (1 - 0.9)/(2) = 0.95`. So we have T = 1.685

The margin of error is:

`M = T(s)/(√(n)) = 1.685(60)/(√(40)) = 16`

In which s is the standard deviation of the sample and n is the size of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 320 - 16 = 304 minutes

The upper end of the interval is the sample mean added to M. So it is 320 + 16 = 336 minutes

The 90% confidence interval for the mean time that the drug will take to reduce all fevers for all people is between 304 minutes and 336 minutes