Question

A sample of 235 observations is selected from a normal population with a population standard deviation of 25. The sample mean is 20.

1. Determine the standard error of the mean. (Round your answer to 3 decimal places.)
2. Determine the 90% confidence interval for the population mean. (Use z Distribution Table.) (Round your answers to 3 decimal places.)

Answer 1

Sample size = n = 235

Sample mean = = 20

Population standard deviation = = 25

a)The standard error of the mean is

b) We have to construct a 90% confidence interval for the population mean.

Here population standard deviation is known so we have to use one sample z-confidence interval.

z confidence interval

Here E is a margin of error

Zc = 1.64 ( Using z table)

So confidence interval is ( 20 - 2.6745 , 20 + 2.6745) = > ( 17.325 , 22.675)