Question

A research scholar wants to know how many times per hour a certain strand of virus reproduces. The mean is found to be 12.9 reproductions and the population standard deviation is known to be 2.2. If a sample of 358 was used for the study, construct the 90

Answer 1

A 90% confidence interval for the mean number of reproductions per hour of the virus strand is approximately (12.65, 13.15).

Step-by-step explanation:

To construct a 90% confidence interval for the mean number of virus reproductions per hour, we use the formula:

`\[ \bar{x} \pm Z \left( (\sigma)/(√(n)) \right) \]`

where:

`- \(\bar{x}\)` is the sample mean (12.9),

`- \(Z\)` is the Z-score corresponding to the desired confidence level (for 90%, it is 1.645),

`- \(\sigma\)` is the population standard deviation (2.2),

`- \(n\)` is the sample size (358).

Substituting these values, we get:

`\[ 12.9 \pm 1.645 \left( (2.2)/(√(358)) \right) \]`

Calculating the interval bounds gives us (12.65, 13.15). This means we are 90% confident that the true mean number of virus reproductions per hour falls within this interval.

In the context of the study, this implies that if we were to conduct the same study multiple times and construct a 90% confidence interval for each, we would expect the true mean to be captured by the interval in 90% of those studies. It provides a range within which we can reasonably estimate the population mean based on our sample data.