Question

As Economic Analyst for High Desert Bank, analyze the amounts of commercial, consumers, and real estate loans.

Population
Mean	63668.57
Standard Deviation	35989.61
Count	350

Commercial Sample
Mean	61780.70
Standard Deviation	35620.92
Count	171

Consumer Sample
Mean	61439.66
Standard Deviation	36977.32
Count	116

Real Estate Sample
Mean	72896.83
Standard Deviation	34206.58
Count	63

Table 4: High Desert Bank Loan Amounts
Tuition Fees	Population	Commercial	Consumer	Real Estate
Mean	63668.57	61780.70	61439.66	72896.83
St. Deviation	35989.61	35620.92	36977.32	34206.58
Confidence Interval
Confidence Interval

1. Construct two 95% confidence intervals for each sample.

• Apply the population standard deviation (σ) in the formula to form z-distribution since the population standard deviation is known.
• Apply the sample standard deviation (s) in the formula to form t-distribution assuming the population standard deviation is unknown.

Answer 1

n : Sample size

for 95% confidence level = (100-95)/100 =0.5 ; /2 = 0.025 ; Z_/2 = Z_0.025 = 1.96

95% confidence interval when population standard deviation is known.

95% confidence interval : Population

95% confidence interval : Commercial

95% confidence interval : Consumer

95% confidence interval : Real Estate

95% confidence interval when population standard deviation is not known.

95% confidence interval : Population :

t_{0.025,349}

1.9668

95% confidence interval : Commercial

t_{0.025,170}

1.974

95% confidence interval : :Consumer

t_{0.025,115}

1.9808

95% confidence interval : :Real Estate

t_{0.025,62}

1.999

Tuition Fees	Population	Commercial	Consumer	Real Estate
Mean	63668.57	61780.7	61439.66	72896.83
St. Deviation	35989.61	35620.92	36977.32	34206.58
Confidence Interval	(59898.0679,67439.0721)	(56441.6603,67119.7397)	(54710.4744,68168.8456)	(64449.967,81343.693)
Confidence Interval	(59884.9865,67452.1535)	(56403.5243,67157.8757)	(54639.0626,68240.2574)	(64281.8916,81511.7684)