How large a sample is needed to be 90% confident that the sample mean interest rate for a 30 year fixed mortgage is within .02% of the true mean 3. Mariana would like to purchase a home and is interested in finding out the average interest ratefor a 30-year fixed mortgage. Bankrate.com states that the population standard deviation for a 30-year fixed mortgage interest rate is .13%. Mariana does some research and collects a simplerandom sample of 24 interest rates for a 30-year fixed mortgage and finds that the average interestrate is 2.99%. Assume that the data is normally distributed.

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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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How large a sample is needed to be 90% confident that the sample mean interest rate for a 30 year fixed mortgage is within .02% of the true mean

3. Mariana would like to purchase a home and is interested in finding out the average interest rate
for a 30-year fixed mortgage. Bankrate.com states that the population standard deviation for a 30-
year fixed mortgage interest rate is .13%. Mariana does some research and collects a simple
random sample of 24 interest rates for a 30-year fixed mortgage and finds that the average interest
rate is 2.99%. Assume that the data is normally distributed.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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