According to a leasing firm's reports, the mean number of miles driven annually in its leased cars is 12,260 miles with a standard deviation of 1380 miles. The company recently starting using new contracts which require customers to have the cars serviced at their own expense. The company's owner believes the mean number of miles driven annually under the new contracts, μ, is less than 12,260 miles. He takes a random sample of 27 cars under the new contracts. The cars in the sample had a mean of 12,088 annual miles driven. Assume that the population is normally distributed. Is there support for the claim, at the 0.10 level of significance, that the population mean number of miles driven annually by cars under the new contracts, is less than 12,260 miles? Assume that the population standard deviation of miles driven annually was not affected by the change to the contracts. Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places, and round your responses as specified below. a. State the null hypothesis H0 and the alternative hypothesis H1. b. Find the value of the test statistic. (Round to three or more decimal places.) c. Find the p-value. (Round to three or more decimal places.) d. Can we support the claim that the population mean number of miles driven annually by cars under the new contracts is less than 12,260 miles?

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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According to a leasing firm's reports, the mean number of miles driven annually in its leased cars is 12,260 miles with a standard deviation of 1380 miles. The company recently starting using new contracts which require customers to have the cars serviced at their own expense. The company's owner believes the mean number of miles driven annually under the new contracts, μ, is less than 12,260 miles. He takes a random sample of 27 cars under the new contracts. The cars in the sample had a mean of 12,088 annual miles driven. Assume that the population is normally distributed. Is there support for the claim, at the 0.10 level of significance, that the population mean number of miles driven annually by cars under the new contracts, is less than 12,260 miles? Assume that the population standard deviation of miles driven annually was not affected by the change to the contracts. Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places, and round your responses as specified below.

a. State the null hypothesis H0 and the alternative hypothesis H1.

b. Find the value of the test statistic. (Round to three or more decimal places.)

c. Find the p-value. (Round to three or more decimal places.)

d. Can we support the claim that the population mean number of miles driven annually by cars under the new contracts is less than 12,260 miles?

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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