Question

A research scientist wants to know how many times per hour a certain strand of bacteria reproduces. The mean is found to be 7.8 reproductions and the population standard deviation is known to be 2.2. If a sample of 697 was used for the study, construct the 85% confidence interval for the true mean number of reproductions per hour for the bacteria. Round your answers to one decimal place.

Answer 1

The 85% confidence interval is ( 7.7 , 8.0 )

Explanation:

In order to find the 85% confidence interval you use the following formula:

`\overline{x}\pm Z_(\alpha/2)(\sigma)/(√(n))` (1)

where

`\overline{x}`: mean of number of bacteria reproduces per hour = 7.8

σ: standard deviation = 2.2

n: sample size = 967

α: 1 - 0.85 = 0.15

Zα/2: Z factor of the density distribution = 1.44

You replace the values of all parameters in the equation (1):

`7.8\pm (1.44)(2.2)/(√(697))\\\\7.8\pm0.119\\\\`

Then, the confidence interval is:

`(7.8-0.119,7.8+0.119)\\\\(7.7,8.0)`