Question

The days of training a new employee needs are normally distributed with a population standard deviation of 3 days and an unknown population mean. If a random sample of 23 new employees is taken and results in a sample mean of 18 days, use a calculator to find a 90% confidence interval for the population mean.

Answer 1

90% confidence interval for the population mean

(16.971 , 19.029)

Explanation:

Step(i):-

Given mean of the sample x⁻ = 18 days

Standard deviation of the Population 'σ' = 3 days

Given sample size 'n' =23

Step(ii):-

90% confidence interval for the population mean is determined by

`((x^(-) - Z_(0.10) (S.D)/(√(n) ) , x^(-) + Z_(0.10) (S.D)/(√(n) ) )`

Critical value Z = 1.645

`((18 - 1.645 (3)/(√(23) ) , 18+ 1.645 (3)/(√(23) ) )`

(18 -1.029 , 18 + 1.029)

(16.971 , 19.029)

final answer:-

90% confidence interval for the population mean

(16.971 , 19.029)