Citrus Rental is a popular car rental agency that has a history of having too few cars available, so that its available cars are overdriven. The mean monthly mileage over the years for Citrus cars has been about 1500 miles per month. Recently, though, Citrus purchased thousands of new cars, and the company claims that the average mileage of its cars is now less than in the past. To test this, a random sample of 14 recent mileages of Citrus cars was taken. The mean of these 14 mileages was 1375 miles per month, and the standard deviation was 220 miles per month. Assume that the population of recent monthly mileages of Citrus cars is normally distributed. At the 0.1 level of significance, can it be concluded that the mean recent monthly mileage, μ, of Citrus cars is less than 1500 miles per month? Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places and round your answers as specified in the table. a) State the null hypothesis H0? and the alternative hypothesis H1 ? . H0:? H1:? (b) Determine the type of test statistic to use. ▼(Choose one) z ? chi square .? f ? t? (c) Find the value of the test statistic. ? (Round to three or more decimal places.) (d) Find the p-value. ? (Round to three or more decimal places.) (e) At the 0.1 level of significance, can it be concluded that the mean recent monthly mileage of Citrus cars is less than 1500 miles per month? yes or no ? Yes No

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Description: Citrus Rental is a popular car rental agency that has a history of having too few cars available, so that its available cars are overdriven. The mean monthly mileage over the years for Citrus cars has been about 1500 miles per month. Recently, though

MATLAB: An Introduction with Applications

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ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

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Citrus Rental is a popular car rental agency that has a history of having too few cars available, so that its available cars are overdriven. The mean monthly mileage over the years for Citrus cars has been about 1500 miles per month. Recently, though, Citrus purchased thousands of new cars, and the company claims that the average mileage of its cars is now less than in the past. To test this, a random sample of 14 recent mileages of Citrus cars was taken. The mean of these 14 mileages was 1375 miles per month, and the standard deviation was 220 miles per month.

Assume that the population of recent monthly mileages of Citrus cars is normally distributed. At the 0.1 level of significance, can it be concluded that the mean recent monthly mileage,

μ, of Citrus cars is less than

1500 miles per month?

Perform a one-tailed test. Then complete the parts below.

Carry your intermediate computations to three or more decimal places and round your answers as specified in the table.

a)	State the null hypothesis H0? and the alternative hypothesis H1 ? .
H0:?
H1:?
(b)	Determine the type of test statistic to use.
	▼(Choose one) z ? chi square .? f ? t?
(c)	Find the value of the test statistic. ? (Round to three or more decimal places.)

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

(e)	At the 0.1 level of significance, can it be concluded that the mean recent monthly mileage of Citrus cars is less than 1500 miles per month? yes or no ?
Yes No

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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a) Hypothesis:

The null hypothesis is,

$H_{0} : μ = 1500$

The alternative hypothesis is,

$H_{1} : μ < 1500$

Here, the mean is to be tested assuming that the population of recent monthly mileages of Citrus cars is normally distributed with unknown population standard deviation.

The appropriate test for testing mean with unknown population standard deviation is t test.

Answer:

Thus, the type of test statistic to be used is t.

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