Question

50 Observations are randomly selected from a normally distributed population with a population standard deviation of 25 and a sample mean of 175. Find a 95% confidence interval for the mean.

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 175

Population standard deviation =    = 25

Sample size = n = 50

At 95% confidence level

= 1 - 95%  

= 1 - 0.95 =0.05

/2 = 0.025

Z/2 = Z_{0.025 = 1.96}

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

= 1.96 * (25 /   50)

= 6.93

At 95% confidence interval estimate of the population mean is,

  ± E

175 ±  6.93   

( 168.07 , 181.93 )