Suppose the mean price for used cars is $10,198. A manager of a Kansas City used car dealership reviewed a sample of 50 recent used car sales at the dealership in an attempt to determine whether the population mean price for used cars at this particular dealership differed from the national mean. The prices for the sample of 50 cars are shown in the file named UsedCars. 12,400 10,400 12,100 10,000 11,000 8,895 7,675 9,975 6,350 10,470 9,895 11,250 8,795 12,500 9,340 10,150 9,200 9,395 11,000 10,640 10,000 7,500 8,000 10,440 10,200 10,300 9,740 9,280 10,930 8,000 9,000 7,680 9,400 10,730 7,350 12,240 11,970 8,240 9,910 10,080 9,440 8,970 9,500 10,050 10,130 11,400 8,500 7,500 9,090 10,500 (a) Formulate the hypotheses that can be used to determine whether a difference exists in the mean price for used cars at the dealership. H0: ? ≤ 10,198 Ha: ? > 10,198 H0: ? < 10,198 Ha: ? ≥ 10,198 H0: ? = 10,198 Ha: ? ≠ 10,198 H0: ? > 10,198 Ha: ? ≤ 10,198 H0: ? ≥ 10,198 Ha: ? < 10,198 (b) What is the test statistic? (Round your answer to three decimal places.) What is the p-value? (Round your answer to four decimal places.) p-value = (c) At ? = 0.05, what is your conclusion? Do not reject H0. There is sufficient evidence to conclude that the population mean price at this dealership differs from the national mean price of 10,198. Do not reject H0. There is insufficient evidence to conclude that the population mean price at this dealership differs from the national mean price of 10,198. Reject H0. There is insufficient evidence to conclude that the population mean price at this dealership differs from the national mean price of 10,198. Reject H0. There is sufficient evidence to conclude that the population mean price at this dealership differs from the national mean price of 10,198.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.1: Measures Of Center

Problem 25PFA

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Suppose the mean price for used cars is $10,198. A manager of a Kansas City used car dealership reviewed a sample of 50 recent used car sales at the dealership in an attempt to determine whether the population mean price for used cars at this particular dealership differed from the national mean. The prices for the sample of 50 cars are shown in the file named UsedCars.

12,400	10,400	12,100	10,000	11,000	8,895	7,675	9,975	6,350	10,470
9,895	11,250	8,795	12,500	9,340	10,150	9,200	9,395	11,000	10,640
10,000	7,500	8,000	10,440	10,200	10,300	9,740	9,280	10,930	8,000
9,000	7,680	9,400	10,730	7,350	12,240	11,970	8,240	9,910	10,080
9,440	8,970	9,500	10,050	10,130	11,400	8,500	7,500	9,090	10,500

(a)

Formulate the hypotheses that can be used to determine whether a difference exists in the mean price for used cars at the dealership.

H₀: ? ≤ 10,198

H_a: ? > 10,198

H₀: ? < 10,198

H_a: ? ≥ 10,198

H₀: ? = 10,198

H_a: ? ≠ 10,198

H₀: ? > 10,198

H_a: ? ≤ 10,198

H₀: ? ≥ 10,198

H_a: ? < 10,198

(b)

What is the test statistic? (Round your answer to three decimal places.)

What is the p-value? (Round your answer to four decimal places.)

p-value =

(c)

At ? = 0.05, what is your conclusion?

Do not reject H₀. There is sufficient evidence to conclude that the population mean price at this dealership differs from the national mean price of 10,198.

Do not reject H₀. There is insufficient evidence to conclude that the population mean price at this dealership differs from the national mean price of 10,198.

Reject H₀. There is insufficient evidence to conclude that the population mean price at this dealership differs from the national mean price of 10,198.

Reject H₀. There is sufficient evidence to conclude that the population mean price at this dealership differs from the national mean price of 10,198.

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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