Question

A research scientist wants to know how many times per hour a certain strand of bacteria reproduces. The mean is found to be 10.3 reproductions and the population standard deviation is known to be 2.1. If a sample of 728 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

Answer:

Confidence interval for the true mean number of reproductions per hour for the bacteria is (10.1,10.5).

Step-by-step explanation:

We are given the following in the question:

Population mean, μ = 10.3

Population standard deviation, σ = 2.1

Sample size, n = 728

Alpha, α = 0.01

Confidence interval:

$\mu \pm z_{critical}\frac{\sigma}{\sqrt{n}}$

Putting the values, we get,

$z_{critical}\text{ at}~\alpha_{0.01} = \pm 2.58$

$10.3 \pm 2.58(\frac{2.1}{\sqrt{728}} ) = 10.3 \pm 0.2008 = (10.0992,10.5008) \approx (10.1,10.5)$