Question

A sample of 245 observations is selected from a normal population with a population standard deviation of 25. The sample mean is 20.

Determine the standard error of the mean. (Round your answer to 3 decimal places.)

Determine the 90% confidence interval for the population mean. (Use z Distribution Table.) (Round your answers to 3 decimal places.)

Answer 1

Given that,

Point estimate = sample mean = = 20

Population standard deviation =    = 25

Sample size = n =245

At 90% confidence level

= 1-0.90% =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 * ( 25 /  245 )

Standard error = 1.597

= 1.645*1.597

=2.627

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

- E < < + E

20 - 2.627 <    < 20 + 2.627

17.373<   < 22.627

(17.373 ,22.627 )