Question
In: Statistics and Probability
Construct two 95% confidence intervals for each sample. SD = $35,989.61 Apply the population standard deviation...
Construct two 95% confidence intervals for each sample.
| SD = | $35,989.61 |
Apply the population standard deviation (σ) in the formula to form z-distribution since the population standard deviation is known.
| Loan Amount | Type Sample 1 |
| $ 30,500.00 | Commercial |
| $ 78,500.00 | Commercial |
| $ 90,000.00 | Commercial |
| $ 19,000.00 | Commercial |
| $ 36,000.00 | Commercial |
| $ 89,500.00 | Commercial |
| $ 22,000.00 | Commercial |
| $ 65,000.00 | Commercial |
| $ 109,000.00 | Commercial |
| $ 5,500.00 | Commercial |
| $ 93,500.00 | Commercial |
| $ 6,000.00 | Commercial |
| $ 85,500.00 | Commercial |
| $ 98,000.00 | Commercial |
| $ 57,000.00 | Commercial |
| $ 59,000.00 | Commercial |
| $ 8,500.00 | Commercial |
| $ 9,000.00 | Commercial |
| $ 16,000.00 | Commercial |
| $ 71,000.00 | Commercial |
| $ 79,000.00 | Commercial |
| $ 32,500.00 | Commercial |
| $ 3,500.00 | Commercial |
| $ 95,500.00 | Commercial |
| $ 75,500.00 | Commercial |
| $ 90,500.00 | Commercial |
| $ 25,500.00 | Commercial |
| $ 122,000.00 | Commercial |
| $ 27,500.00 | Commercial |
| $ 112,500.00 | Commercial |
| $ 91,000.00 | Commercial |
| $ 107,500.00 | Commercial |
| $ 75,500.00 | Commercial |
| $ 73,000.00 | Commercial |
| $ 17,500.00 | Commercial |
| $ 91,000.00 | Commercial |
| $ 23,500.00 | Commercial |
| $ 111,000.00 | Commercial |
| $ 66,500.00 | Commercial |
| $ 21,000.00 | Commercial |
| $ 21,500.00 | Commercial |
| $ 12,000.00 | Commercial |
| $ 45,000.00 | Commercial |
| $ 123,000.00 | Commercial |
| $ 18,500.00 | Commercial |
| $ 6,500.00 | Commercial |
| $ 118,500.00 | Commercial |
| $ 91,000.00 | Commercial |
| $ 23,000.00 | Commercial |
| $ 38,500.00 | Commercial |
| $ 96,000.00 | Commercial |
| $ 91,000.00 | Commercial |
| $ 16,500.00 | Commercial |
| $ 36,000.00 | Commercial |
| $ 96,000.00 | Commercial |
| $ 96,500.00 | Commercial |
| $ 86,500.00 | Commercial |
| $ 46,000.00 | Commercial |
| $ 19,000.00 | Commercial |
| $ 84,500.00 | Commercial |
| $ 57,000.00 | Commercial |
| $ 29,000.00 | Commercial |
| $ 124,500.00 | Commercial |
| $ 12,000.00 | Commercial |
| $ 50,000.00 | Commercial |
| $ 66,000.00 | Commercial |
| $ 48,000.00 | Commercial |
| $ 44,000.00 | Commercial |
| $ 92,000.00 | Commercial |
| $ 16,000.00 | Commercial |
| $ 39,500.00 | Commercial |
| $ 9,000.00 | Commercial |
| $ 43,000.00 | Commercial |
| $ 91,000.00 | Commercial |
| $ 73,000.00 | Commercial |
| $ 90,500.00 | Commercial |
| $ 64,500.00 | Commercial |
| $ 112,500.00 | Commercial |
| $ 82,500.00 | Commercial |
| $ 86,500.00 | Commercial |
| $ 10,000.00 | Commercial |
| $ 31,500.00 | Commercial |
| $ 41,500.00 | Commercial |
| $ 39,000.00 | Commercial |
| $ 40,500.00 | Commercial |
| $ 69,000.00 | Commercial |
| $ 66,500.00 | Commercial |
| $ 60,000.00 | Commercial |
| $ 54,000.00 | Commercial |
| $ 122,000.00 | Commercial |
| $ 44,000.00 | Commercial |
| $ 33,000.00 | Commercial |
| $ 97,000.00 | Commercial |
| $ 103,000.00 | Commercial |
| $ 97,500.00 | Commercial |
| $ 110,500.00 | Commercial |
| $ 21,500.00 | Commercial |
| $ 116,000.00 | Commercial |
| $ 72,000.00 | Commercial |
| $ 66,500.00 | Commercial |
| $ 79,000.00 | Commercial |
| $ 36,000.00 | Commercial |
| $ 84,000.00 | Commercial |
| $ 99,000.00 | Commercial |
| $ 4,000.00 | Commercial |
| $ 115,000.00 | Commercial |
| $ 86,000.00 | Commercial |
| $ 42,000.00 | Commercial |
| $ 117,000.00 | Commercial |
| $ 18,500.00 | Commercial |
| $ 123,000.00 | Commercial |
| $ 109,000.00 | Commercial |
| $ 37,500.00 | Commercial |
| $ 53,500.00 | Commercial |
| $ 36,000.00 | Commercial |
| $ 62,000.00 | Commercial |
| $ 44,500.00 | Commercial |
| $ 3,500.00 | Commercial |
| $ 56,500.00 | Commercial |
| $ 82,000.00 | Commercial |
| $ 7,500.00 | Commercial |
| $ 94,000.00 | Commercial |
| $ 89,000.00 | Commercial |
| $ 6,500.00 | Commercial |
| $ 9,500.00 | Commercial |
| $ 89,000.00 | Commercial |
| $ 6,500.00 | Commercial |
| $ 95,500.00 | Commercial |
| $ 23,500.00 | Commercial |
| $ 59,000.00 | Commercial |
| $ 31,000.00 | Commercial |
| $ 22,500.00 | Commercial |
| $ 35,000.00 | Commercial |
| $ 59,000.00 | Commercial |
| $ 31,500.00 | Commercial |
| $ 40,500.00 | Commercial |
| $ 73,500.00 | Commercial |
| $ 21,500.00 | Commercial |
| $ 45,000.00 | Commercial |
| $ 79,500.00 | Commercial |
| $ 110,500.00 | Commercial |
| $ 112,000.00 | Commercial |
| $ 12,500.00 | Commercial |
| $ 105,000.00 | Commercial |
| $ 92,500.00 | Commercial |
| $ 65,000.00 | Commercial |
| $ 7,500.00 | Commercial |
| $ 6,000.00 | Commercial |
| $ 73,500.00 | Commercial |
| $ 98,500.00 | Commercial |
| $ 59,500.00 | Commercial |
| $ 31,000.00 | Commercial |
| $ 67,000.00 | Commercial |
| $ 28,500.00 | Commercial |
| $ 63,500.00 | Commercial |
| $ 108,500.00 | Commercial |
| $ 101,000.00 | Commercial |
| $ 120,000.00 | Commercial |
| $ 63,500.00 | Commercial |
| $ 74,000.00 | Commercial |
| $ 40,000.00 | Commercial |
| $ 109,500.00 | Commercial |
| $ 114,500.00 | Commercial |
| $ 89,000.00 | Commercial |
| $ 86,000.00 | Commercial |
| $ 69,500.00 | Commercial |
| $ 85,000.00 | Commercial |
| $ 5,500.00 | Commercial |
| $ 112,500.00 | Commercial |
| $ 95,000.00 | Commercial |
| $ 70,500.00 | Commercial |
| $ 33,000.00 | Consumer |
| $ 89,500.00 | Consumer |
| $ 40,000.00 | Consumer |
| $ 76,000.00 | Consumer |
| $ 72,500.00 | Consumer |
| $ 123,500.00 | Consumer |
| $ 9,000.00 | Consumer |
| $ 6,500.00 | Consumer |
| $ 113,500.00 | Consumer |
| $ 86,000.00 | Consumer |
| $ 108,500.00 | Consumer |
| $ 24,500.00 | Consumer |
| $ 78,000.00 | Consumer |
| $ 70,000.00 | Consumer |
| $ 125,000.00 | Consumer |
| $ 32,500.00 | Consumer |
| $ 15,000.00 | Consumer |
| $ 16,000.00 | Consumer |
| $ 40,500.00 | Consumer |
| $ 101,000.00 | Consumer |
| $ 12,000.00 | Consumer |
| $ 33,000.00 | Consumer |
| $ 50,000.00 | Consumer |
| $ 81,500.00 | Consumer |
| $ 17,500.00 | Consumer |
| $ 45,000.00 | Consumer |
| $ 56,500.00 | Consumer |
| $ 39,000.00 | Consumer |
| $ 123,500.00 | Consumer |
| $ 118,000.00 | Consumer |
| $ 46,500.00 | Consumer |
| $ 49,000.00 | Consumer |
| $ 105,500.00 | Consumer |
| $ 15,500.00 | Consumer |
| $ 94,500.00 | Consumer |
| $ 20,000.00 | Consumer |
| $ 83,500.00 | Consumer |
| $ 74,000.00 | Consumer |
| $ 33,000.00 | Consumer |
| $ 122,500.00 | Consumer |
| $ 64,000.00 | Consumer |
| $ 11,500.00 | Consumer |
| $ 124,000.00 | Consumer |
| $ 33,000.00 | Consumer |
| $ 14,500.00 | Consumer |
| $ 11,500.00 | Consumer |
| $ 83,500.00 | Consumer |
| $ 101,000.00 | Consumer |
| $ 62,000.00 | Consumer |
| $ 75,500.00 | Consumer |
| $ 18,500.00 | Consumer |
| $ 56,000.00 | Consumer |
| $ 66,500.00 | Consumer |
| $ 42,500.00 | Consumer |
| $ 44,500.00 | Consumer |
| $ 72,500.00 | Consumer |
| $ 20,000.00 | Consumer |
| $ 37,500.00 | Consumer |
| $ 5,500.00 | Consumer |
| $ 94,000.00 | Consumer |
| $ 98,000.00 | Consumer |
| $ 94,000.00 | Consumer |
| $ 57,500.00 | Consumer |
| $ 30,000.00 | Consumer |
| $ 120,500.00 | Consumer |
| $ 8,000.00 | Consumer |
| $ 108,500.00 | Consumer |
| $ 6,000.00 | Consumer |
| $ 106,500.00 | Consumer |
| $ 31,000.00 | Consumer |
| $ 52,500.00 | Consumer |
| $ 58,500.00 | Consumer |
| $ 105,000.00 | Consumer |
| $ 4,500.00 | Consumer |
| $ 76,500.00 | Consumer |
| $ 72,500.00 | Consumer |
| $ 107,000.00 | Consumer |
| $ 98,500.00 | Consumer |
| $ 87,000.00 | Consumer |
| $ 118,500.00 | Consumer |
| $ 105,000.00 | Consumer |
| $ 64,500.00 | Consumer |
| $ 16,500.00 | Consumer |
| $ 77,500.00 | Consumer |
| $ 40,000.00 | Consumer |
| $ 16,000.00 | Consumer |
| $ 111,000.00 | Consumer |
| $ 41,000.00 | Consumer |
| $ 7,000.00 | Consumer |
| $ 35,000.00 | Consumer |
| $ 90,000.00 | Consumer |
| $ 21,500.00 | Consumer |
| $ 71,500.00 | Consumer |
| $ 115,500.00 | Consumer |
| $ 17,500.00 | Consumer |
| $ 8,500.00 | Consumer |
| $ 72,000.00 | Consumer |
| $ 56,500.00 | Consumer |
| $ 45,500.00 | Consumer |
| $ 49,000.00 | Consumer |
| $ 43,500.00 | Consumer |
| $ 124,000.00 | Consumer |
| $ 41,000.00 | Consumer |
| $ 10,500.00 | Consumer |
| $ 102,000.00 | Consumer |
| $ 113,500.00 | Consumer |
| $ 36,500.00 | Consumer |
| $ 15,000.00 | Consumer |
| $ 114,500.00 | Consumer |
| $ 121,500.00 | Consumer |
| $ 76,000.00 | Consumer |
| $ 64,500.00 | Consumer |
| $ 27,000.00 | Consumer |
| $ 77,500.00 | Consumer |
| $ 63,500.00 | Consumer |
| $ 76,500.00 | Consumer |
| $ 48,500.00 | Real Estate |
| $ 117,500.00 | Real Estate |
| $ 57,000.00 | Real Estate |
| $ 82,000.00 | Real Estate |
| $ 118,000.00 | Real Estate |
| $ 70,000.00 | Real Estate |
| $ 106,000.00 | Real Estate |
| $ 56,500.00 | Real Estate |
| $ 39,000.00 | Real Estate |
| $ 119,000.00 | Real Estate |
| $ 93,000.00 | Real Estate |
| $ 11,000.00 | Real Estate |
| $ 66,000.00 | Real Estate |
| $ 19,500.00 | Real Estate |
| $ 106,500.00 | Real Estate |
| $ 23,000.00 | Real Estate |
| $ 98,500.00 | Real Estate |
| $ 30,500.00 | Real Estate |
| $ 120,500.00 | Real Estate |
| $ 82,500.00 | Real Estate |
| $ 102,500.00 | Real Estate |
| $ 22,000.00 | Real Estate |
| $ 112,500.00 | Real Estate |
| $ 112,000.00 | Real Estate |
| $ 24,500.00 | Real Estate |
| $ 57,000.00 | Real Estate |
| $ 74,000.00 | Real Estate |
| $ 102,500.00 | Real Estate |
| $ 29,000.00 | Real Estate |
| $ 81,500.00 | Real Estate |
| $ 34,000.00 | Real Estate |
| $ 112,000.00 | Real Estate |
| $ 68,000.00 | Real Estate |
| $ 109,500.00 | Real Estate |
| $ 32,000.00 | Real Estate |
| $ 32,000.00 | Real Estate |
| $ 99,000.00 | Real Estate |
| $ 93,500.00 | Real Estate |
| $ 95,000.00 | Real Estate |
| $ 89,000.00 | Real Estate |
| $ 83,000.00 | Real Estate |
| $ 117,000.00 | Real Estate |
| $ 58,000.00 | Real Estate |
| $ 12,500.00 | Real Estate |
| $ 102,500.00 | Real Estate |
| $ 81,000.00 | Real Estate |
| $ 125,000.00 | Real Estate |
| $ 63,500.00 | Real Estate |
| $ 107,500.00 | Real Estate |
| $ 9,000.00 | Real Estate |
| $ 110,500.00 | Real Estate |
| $ 64,500.00 | Real Estate |
| $ 69,500.00 | Real Estate |
| $ 71,000.00 | Real Estate |
| $ 81,500.00 | Real Estate |
| $ 89,000.00 | Real Estate |
| $ 61,500.00 | Real Estate |
| $ 65,000.00 | Real Estate |
| $ 123,000.00 | Real Estate |
| $ 65,000.00 | Real Estate |
| $ 45,000.00 | Real Estate |
| $ 25,000.00 | Real Estate |
| $ 17,000.00 |
Real Estate |
Solutions
Expert Solution
GIVEN:
Population standard deviation 
When the population standard deviation is known, the formula for a confidence interval (CI) for a population mean is given by,
where 
is the sample mean.
is the population standard deviation.
n is the sample size, and
z* represents the appropriate z*-value from the standard normal distribution for desired confidence level.
For the given problem the z*-value from the standard normal distribution for 95% confidence level is 1.96.
SAMPLE 1 (COMMERCIAL TYPE):
Let us consider sample 1 (commercial type)
Total number of observations from sample 1 (n) = 171
The sample mean is defined as the average of n observations from the sample and it is considered to be the estimate of pupulation mean.
I have used excel function to find the sample mean given by,
"=AVERAGE(select array of values from sample 1)"
Thus the mean of sample 1 
Population standard deviation
The z*-value from the standard normal distribution for 95% confidence level is 1.96.
The 95% confidence interval (CI) for a population mean is given by,
Thus
95% confidence interval for mean loan amount in the sample 1
(Commercial Type) is 
.
SAMPLE 2 (CONSUMER TYPE):
Let us consider sample 2 (consumer type)
Total number of observations from sample 2 (n) = 116
The sample mean is defined as the average of n observations from the sample and it is considered to be the estimate of pupulation mean.
I have used excel function to find the sample mean given by,
"=AVERAGE(select array of values from sample 2)"
Thus
the mean of sample 2 
Population standard deviation
The z*-value from the standard normal distribution for 95% confidence level is 1.96.
The 95% confidence interval (CI) for a population mean is given by,
Thus
95% confidence interval for mean loan amount in the sample 2
(Consumer Type) is 
SAMPLE 3 (REAL ESTATE TYPE):
Let us consider sample 3 (Real estate type)
Total number of observations from sample 3 (n) = 63
The sample mean is defined as the average of n observations from the sample and it is considered to be the estimate of pupulation mean.
I have used excel function to find the sample mean given by,
"=AVERAGE(select array of values from sample 2)"
Thus
the mean of sample 3 
Population standard deviation
The z*-value from the standard normal distribution for 95% confidence level is 1.96.
The 95% confidence interval (CI) for a population mean is given by,
Thus
95% confidence interval for mean loan amount in the sample 3 (Real
Estate Type) is 
orchestra answered 2 years agoRelated Solutions
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