In: Math
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.
( , )
Solution :
Given that,
Point estimate = sample mean =
= 30
Population standard deviation =
= 20
Sample size = n =10
At 95% confidence level the z is ,
Margin of error = E = Z/2
* (
/
n)
= 1.96* (20 / 10
)
= 12.4
At 95% confidence interval estimate of the population mean
is,
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 ,
Margin of error = E = Z/2
* (
/
n)
= 1.96* (20 / 100
)
= 3.92
At 95% confidence interval estimate of the population mean
is,
30 -3.92<
< 30 + 3.92
26.08<
< 33.92
( 26.08 , 33.92 )