Question

A research scientist wants to know how many times per hour a certain strand of bacteria reproduces. The mean is found to be 7.3 reproductions and the population standard deviation is known to be 1.9. If a sample of 150 was used for the study, construct the 80% 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 =     = 7.3

Population standard deviation =    = 1.9

Sample size n =150

At 80% confidence level the z is ,

= 1 - 80% = 1 - 0.80 = 0.20

/ 2 = 0.10

Z/2 = Z0.10= 1.28 ( Using z table )

Margin of error = E =   Z/2    * ( /n)
= 1.28 * ( 1.9 / 150 )

= 0.199
At 80% confidence interval estimate of the population mean
is,

- E < < + E

7.3 -0.199 <   < 7.3+ 0.199

7.101 <   <7.499

( 7.1 ,7.5)