Question

A simple random sample of 10 items resulted in a sample mean of 30. The population standard deviation is σ=20.

a. Compute the 95% confidence interval for the population mean. Round your answers to one decimal place.
( ,  )

b. Assume that the same sample mean was obtained from a sample of 100 items. Provide a 95% confidence interval for the population mean. Round your answers to two decimal places.
( ,  )

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 30

Population standard deviation =    = 20

Sample size = n =10

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_/2 = Z_0.025 = 1.96

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

= 1.96* (20 /  10 )

= 12.4
At 95% confidence interval estimate of the population mean
is,

- E < < + E

30 -12.4<   < 30 + 12.4

17.6 <   < 42.4

( 17.6 , 42.4 )

(B)

Solution :

Given that,

Point estimate = sample mean = = 30

Population standard deviation =    = 20

Sample size = n =100

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_/2 = Z_0.025 = 1.96

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

= 1.96* (20 /  100 )

= 3.92
At 95% confidence interval estimate of the population mean
is,

- E < < + E

30 -3.92<   < 30 +  3.92

26.08<   < 33.92

( 26.08 , 33.92 )