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Pepsi [2]
3 years ago
9

A research scholar wants to know how many times per hour a certain strand of virus reproduces. The mean is found to be 4 reprodu

ctions and the population standard deviation is known to be 2.3. If a sample of 1083 was used for the study, construct the 99% confidence interval for the true mean number of reproductions per hour for the virus. Round your answers to one decimal place.
Mathematics
1 answer:
Lynna [10]3 years ago
5 0

Answer:

The 99% confidence interval for the true mean number of reproductions per hour for the virus is between 3.8 and 4.2.

Step-by-step explanation:

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

\alpha = \frac{1 - 0.99}{2} = 0.005

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

That 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\frac{\sigma}{\sqrt{n}}

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

M = 2.575\frac{2.3}{\sqrt{1083}} = 0.18

Rounding to one decimal place, 0.2.

The lower end of the interval is the sample mean subtracted by M. So it is 4 - 0.2 = 3.8 reproductions

The upper end of the interval is the sample mean added to M. So it is 4 + 0.2 = 4.2 reproductions.

The 99% confidence interval for the true mean number of reproductions per hour for the virus is between 3.8 and 4.2.

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