In: Math
uConstruct confidence intervals for the population mean of 80%, 90%, 95%, 99% using the following data and a population standard deviation of 900:
un = 100
u?x ̅ = 425
Solution :
Given that,
Point estimate = sample mean =
= 425
Population standard deviation =
= 900
Sample size = n = 100
1) At 80% confidence level
= 1 - 80%
= 1 - 0.80 =0.20
/2
= 0.10
Z/2
= Z0.10 = 1.282
Margin of error = E = Z/2
* (
/n)
= 1.282 * ( 900 / 100
)
= 115.38
At 80% confidence interval estimate of the population mean is,
± E
= 425 ± 115.38
( 309.62, 540.38 )
2) 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 * ( 900 / 100
)
= 148.05
At 90% confidence interval estimate of the population mean is,
± E
= 425 ± 148.05
( 276.95, 573.05 )
3) At 95% confidence level
= 1 - 95%
= 1 - 0.95 =0.05
/2
= 0.025
Z/2
= Z0.025 = 1.96
Margin of error = E = Z/2
* (
/n)
= 1.96 * ( 900 / 100
)
= 176.40
At 95% confidence interval estimate of the population mean is,
± E
= 425 ± 176.40
( 248.60, 601.40 )
4) At 99% confidence level
= 1 - 99%
= 1 - 0.99 =0.01
/2
= 0.005
Z/2
= Z0.005 = 2.576
Margin of error = E = Z/2
* (
/n)
= 2.576 * ( 900 / 100
)
= 231.84
At 99% confidence interval estimate of the population mean is,
± E
= 425 ± 231.84
( 193.16, 656.84 )