In a recent sample of 88 used cars sales costs, the sample mean was $6,525 with a standard deviation of $3,158. Assume the underlying distribution is approximately normal. NOTE: If you are using a Student's t-distribution, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.) Part (a) Which distribution should you use for this problem? (Enter your answer in the form z or tdf where df is the degrees of freedom.) Explain your choice. The standard normal distribution should be used because the population standard deviation is given.The Student's t-distribution with 88 degrees of freedom should be used because the standard deviation of the population is unknown. The Student's t-distribution with 87 degrees of freedom should be used because the standard deviation of the population is unknown.The standard normal distribution should be used because the sample is large. Correct! The standard deviation given is a result of the sample data; therefore, the Student's t-distribution should be used for n − 1 degrees of freedom. Part (b) Part (c) Construct a 95% confidence interval for the population mean cost of a used car. (i) State the confidence interval. (Round your answers to one decimal place.) , (ii) Sketch the graph. (iii) Calculate the error bound. (Round your answer to one decimal place.) Part (d) Additional Materials eBook

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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In a recent sample of 88 used cars sales costs, the sample mean was $6,525 with a standard deviation of $3,158. Assume the underlying distribution is approximately normal.

NOTE: If you are using a Student's t-distribution, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.)

Part (a)

Which distribution should you use for this problem? (Enter your answer in the form z or t_df where df is the degrees of freedom.)

Explain your choice.

The standard normal distribution should be used because the population standard deviation is given.The Student's t-distribution with 88 degrees of freedom should be used because the standard deviation of the population is unknown. The Student's t-distribution with 87 degrees of freedom should be used because the standard deviation of the population is unknown.The standard normal distribution should be used because the sample is large.

Correct! The standard deviation given is a result of the sample data; therefore, the Student's t-distribution should be used for n − 1 degrees of freedom.
Part (b)
Part (c)

Construct a 95% confidence interval for the population mean cost of a used car.
(i) State the confidence interval. (Round your answers to one decimal place.)

,

(ii) Sketch the graph.

(iii) Calculate the error bound. (Round your answer to one decimal place.)
Part (d)

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Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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