Question

A research scientist wants to know how many times per hour a certain strand of bacteria reproduces. The mean is found to be 99 reproductions and the population standard deviation is known to be 22. If a sample of 405 was used for the study, construct the 90% 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,

= 99

= 22

n = 405

At 90% confidence level the z is ,

  = 1 - 90% = 1 - 0.90 = 0.10

/ 2 = 0.10 / 2 = 0.05

Z_/2 = Z_0.05 = 1.645

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

= 1.645 * ( 22/ 405)

= 1.8

At 90% confidence interval estimate of the population mean is,

- E < < + E

99 - 1.8 < < 99+ 1.8

97.2< < 100.8

(97.2,100.8 )