Answered: According to a newspaper, customers are…

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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Question

According to a newspaper, customers are not settling for automobiles straight off the production lines. A sample of 199 recent purchases of a particular car model yielded a sample mean of $4,273 above the $20,200 base sticker price. Suppose the cost of accessories purchased for all cars of this model has a standard deviation of $1,452.

a. Calculate a 90% confidence interval for the average cost of accessories on this model. b. Determine the margin of error in estimating the average cost of accessories on this model. c. What sample size would be required to reduce the margin of error by 50%?

a. The 90% confidence interval for the average cost of accessories on the particular model is from $to $ (Round to the nearest cent as needed. Use ascending order.)

b. The margin of error in estimating the average cost of accessories on the particular model is $ (Round to the nearest cent as needed.)

c. A sample size of (Round up to the nearest integer.) is required to reduce the margin of error by 50%

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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