Question

A sample of 22 observations is selected from a normal population for which the population standard deviation is known to be 8. The sample mean is 27.

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

The standard error of the mean is.

b. Explain why we can use formula (8–1) to determine the 90% confidence interval, even though the sample size is less than 30.

(Click to select)  The population is normally distributed and the population variance is unknown.  The population is normally distributed and the population variance is known.  The population is normally distributed and the sample variance is known.

c. Determine the 90% confidence interval for the population mean. (Round the intermediate calculation to 3 decimal places. Round the final answers to 3 decimal places.)

The 90% confidence interval for the population mean is between and.

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 27

Population standard deviation =    = 8

Sample size = n =22

a) = / n = 8 / 22 = 1.706

b)  The population is normally distributed and the population variance is known.

c) At 90% confidence level

= 1 - 90%  

= 1 - 0.90 =0.10

/2 = 0.05

Z/2 = Z0.05 = 1.645

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

= 1.645 * ( 8 /  22 )

= 2.806

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

  ± E

27 ± 2.806

( 24.194, 29.806 )  

The 90% confidence interval for the population mean is between 24.194 and 29.806.