Question
In: Math
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
* ( 
/
= 1.282 * ( 900 /
= 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
* (
/
= 1.645 * ( 900 /
= 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
* (
/
= 1.96 * ( 900 /
= 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
* (
/
= 2.576 * ( 900 /
= 231.84
At 99% confidence interval estimate of the population mean is,
±
E
= 425 ± 231.84
( 193.16, 656.84 )
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(Round the intermediate values to 4 decimal places. Round your
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90% confidence interval: ?≤ μ ?≤
95% confidence interval: ?≤ μ? ≤
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Construct 90%, 95%, and 99% confidence intervals to estimate μ from the following data. State the...
Construct 90%, 95%, and 99% confidence intervals to estimate
μ from the following data. State the point estimate.
Assume the data come from a normally distributed
population.
13.2
11.6
11.9
12.5
12.5
11.4
12.0
11.7
11.8
13.2
Appendix A Statistical Tables
(Round the intermediate values to 4 decimal places.
Round your answers to 2 decimal places.)
90% confidence interval: enter the lower limit of the 90%
confidence interval ≤ μ ≤ enter the upper limit
of the 90% confidence interval
95%...
Construct 90%, 95%, and 99% confidence intervals to estimate μ from the following data. State the...
Construct 90%, 95%, and 99% confidence intervals to estimate
μ from the following data. State the point estimate.
Assume the data come from a normally distributed
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11.6
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90% confidence interval: enter the lower limit of the 90%
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decimal places. Round your answers to 2 decimal places.) 90%
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Assume the data come from a normally distributed
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12.5
11.6
11.9
12.5
12.5
11.4
12.0
11.7
11.8
12.5
Appendix A Statistical Tables
(Round the intermediate values to 4 decimal places.
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95% confidence interval:
≤ μ ≤
99% confidence interval:
≤ μ ≤
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