Question

A research scientist wants to know how many times per hour a certain strand of bacteria reproduces. The mean is found to be 11 reproductions and the population standard deviation is known to be 2. If a sample of 385 was used for the study, construct the 95% confidence interval for the true mean number of reproductions per hour for the bacteria. Round your answers to one decimal place.

Answer 1

Solution :

Given that,

Point estimate = sample mean =     = 11

Population standard deviation =    = 2

Sample size n =385

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.96   ( Using z table )

Margin of error = E =   Z/2    * ( /n)
= 1.96* ( 2/ 385)

= 0.2
At 95% confidence interval
is,

- E < < + E

11 - 0.2 <   < 11+ 0.2

(10.8 , 11.2)