Question

A sample of 8 observations is selected from a normal population for which the population standard deviation is known to be 4. The sample mean is 19. (Round your answers to 3 decimal places.)

(a)	The standard error of the mean is .

(c)	The 95 percent confidence interval for the population mean is between  and .

Answer 1

Solution :

Given that,

Point estimate = sample mean =     = 19

Population standard deviation =    = 4

Sample size n =8

a.

The standard error of the mean is =( /n) = (4 / 8 )=1.414

b.

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.96   ( Using z table )

Margin of error = E =   Z/2    * ( /n)
= 1.96* (4 / 8 )

= 7.840
At 95% confidence interval mean
is,

- E < < + E

19 - 7.840 <   < 19 + 7.840

11.160 <   < 26.840

( 11.160 , 26.840)

between 11.160 to 26.840