Question

A research scholar wants to know how many times per hour a certain strand of virus reproduces. The mean is found to be 13.7 reproductions and the population standard deviation is know to be 2. If a sample of 205 was used for the study, construct the 80% confidence interval for the true mean number of reproductions per hour for the virus. Round your answers to one decimal place.

Answer 1

Solution :

Given that,

= 13.7

= 2

n = 205

At 80% confidence level the z is ,

  = 1 - 80% = 1 - 0.80 = 0.20

/ 2 = 0.20 / 2 = 0.10

Z_/2 = Z_0.10 = 1.28

Margin of error = E = Z_/2* ( /n)

= 1.28 * (2 / 205)

= 0.2

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

- E < < + E

13.7 - 0.2 < < 13.7 + 0.2

13.5 < < 13.9

(13.5 , 13.9)