Question

In: Statistics and Probability

1. In recent years, due to low interest rates, many homeowners refinanced their home mortgages. Linda...

1. In recent years, due to low interest rates, many homeowners refinanced their home mortgages. Linda is mortgage officer at the bank. Below are the amounts refinanced for 20 loans for the last month per $ 1,000's.

34, 60, 61, 66, 66, 73, 75, 77, 79, 83, 85, 86, 87, 87, 90, 93, 93, 100, 125, 130

a) Find the mea, median, 1st quartile, 3rd quartile, and the IQR of the data. ( IQR = 3rd - 1st quartiles )

b) Find any outliers, if they exist. ( lower: Q1-1.5* IQR and upper: Q3 + 1.5 *IQR )

c) Draw a box plot and label all important values.

d) Without, outliers determine the 92% confidence interval for the population mean, using population standard deviation of 13.2 and the sample mean without outliers.

e) Stated the margin of error for the confidence interval.

Expert Solution

a) Mean = (34 + 60 + 61 + 66 + 66 + 73 + 75 + 77 + 79 + 83 + 85 + 86 + 87 + 87 + 90 + 93 + 93 + 100 + 125 + 130)/20 = 82.5

Median = (83 + 85)/2 = 84

1st quartile = (66 + 73)/2 = 69.5

3rd quartile = (90 + 93)/2 = 91.5

IQR = Q3 - Q1 = 91.5 - 69.5 = 22

b) Lower: Q1 - 1.5 * IQR = 69.5 - 1.5 * 22 = 36.5

Upper = Q3 + 1.5 * IQR = 91.5 + 1.5 * 22 = 124.5

So the outliers are 34, 125, 130

c)

d) The sample mean without outliers is = (60 + 61 + 66 + 66 + 73 + 75 + 77 + 79 + 83 + 85 + 86 + 87 + 87 + 90 + 93 + 93 + 100)/17 = 80.0588

At 92% confidence level, the critical value is z^* = 1.75

The 92% confidence interval is

e) Margin of error is

orchestra answered 2 years ago

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