Homework SourseA realtor in Mission Viejo California wants to estimate the
A realtor in Mission Viejo, California, wants to estimate the average price of a house in the city.
House Price
430
520
460
475
670
521
670
417
533
525
538
370
530
525
430
330
575
555
521
350
399
560
440
425
669
660
702
540
460
588
445
412
735
537
630
430
a.
Open the Excel file using the link above (data are in $1,000s). Assume the population standard deviation is $100 (in $1,000s). Calculate the sample mean. (Do not round intermediate calculations. Round your answer to 2 decimal places.)
b.
Construct a 90% and a 99% confidence interval for the average house price. (Use rounded sample mean. Do not round intermediate calculations. Round \"z\" value and final answers to 2 decimal places.)
Solution
Getting the mean, X,
X = Sum(x) / n
Sum(x) = 18577
As n = 36,
Thus,
X = 516.0277778 = 516.03 [ANSWER]
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B)
Note that
Lower Bound = X - z(alpha/2) * s / sqrt(n)
Upper Bound = X + z(alpha/2) * s / sqrt(n)
where
alpha/2 = (1 - confidence level)/2 = 0.05
X = sample mean = 516.03
z(alpha/2) = critical z for the confidence interval = 1.64
s = sample standard deviation = 100
n = sample size = 36
Thus,
Lower bound = 488.6966667
Upper bound = 543.3633333
Thus, the confidence interval is
( 488.70 , 543.36 ) [ANSWER, 90% CONFIDENCE]
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B)
Note that
Lower Bound = X - z(alpha/2) * s / sqrt(n)
Upper Bound = X + z(alpha/2) * s / sqrt(n)
where
alpha/2 = (1 - confidence level)/2 = 0.005
X = sample mean = 516.03
z(alpha/2) = critical z for the confidence interval = 2.58
s = sample standard deviation = 100
n = sample size = 36
Thus,
Lower bound = 473.03
Upper bound = 559.03
Thus, the confidence interval is
( 473.03 , 559.03 ) [ANSWER, 99% CONFIDENCE INTERVAL]
