Question

A research scholar wants to know how many times per hour a certain strand of virus reproduces. The mean is found to be 10.2 reproductions and the population standard deviation is known to be 2.4. If a sample of 907 was used for the study, construct the 85% confidence interval for the true mean number of reproductions per hour for the virus. Round your answers to one decimal place

Answer 1

The 85% confidence interval for the true mean number of reproductions per hour for the virus is between 10.1 and 10.3.

Explanation:

We have that to find our
`\alpha` level, that is the subtraction of 1 by the confidence interval divided by 2. So:

`\alpha = (1-0.85)/(2) = 0.075`

Now, we have to find z in the Ztable as such z has a pvalue of
`1-\alpha`.

So it is z with a pvalue of
`1-0.075= 0.925`, so
`z = 1.44`

Now, find the margin of error M as such

`M = z*(\sigma)/(√(n))`

In which
`\sigma` is the standard deviation of the population and n is the size of the sample.

`M = 1.44*(2.4)/(√(907)) = 0.1`

The lower end of the interval is the sample mean subtracted by M. So it is 10.2 - 0.1 = 10.1 reproductions per hour.

The upper end of the interval is the sample mean added to M. So it is 10.2 + 0.1 = 10.3 reproductions per hour.

The 85% confidence interval for the true mean number of reproductions per hour for the virus is between 10.1 and 10.3.