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uConstruct confidence intervals for the population mean of 80%, 90%, 95%, 99% using the following data...

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

Solutions

Expert Solution

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 )


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