Question

A research scientist wants to know how many times per hour a certain strand of bacteria reproduces. The mean is found to be 9.8 reproductions and the population standard deviation is known to be 2.4. If a sample of 955 was used for the study, construct the 99% confidence interval for the true mean number of reproductions per hour for the bacteria. Round your answers to one decimal place.

Answer 1

The 99% confidence interval for the true mean number of reproductions per hour for the bacteria is between 9.6 and 10.

Explanation:

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

`\alpha = (1-0.99)/(2) = 0.005`

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
`1-0.005 = 0.995`, so
`z = 2.575`

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 = 2.575(2.4)/(√(955)) = 0.2`

The lower end of the interval is the sample mean subtracted by M. So it is 9.8 - 0.2 = 9.6 reproductions per hour.

The upper end of the interval is the sample mean added to M. So it is 9.8 + 0.2 = 10 reproductions per hour.

The 99% confidence interval for the true mean number of reproductions per hour for the bacteria is between 9.6 and 10.