Question

DATAfile: UsedCars

You may need to use the appropriate technology to answer this question.

Suppose the mean price for used cars is $10,191. 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: μ < 10,191

H_a: μ ≥ 10,191

H₀: μ ≤ 10,191

H_a: μ > 10,191

    

H₀: μ > 10,191

H_a: μ ≤ 10,191

H₀: μ = 10,191

H_a: μ ≠ 10,191

H₀: μ ≥ 10,191

H_a: μ < 10,191

(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

α = 0.05,

what is your conclusion?

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 10,191.

Reject H₀. There is sufficient evidence to conclude that the population mean price at this dealership differs from the national mean price of 10,191.    

Reject H₀. There is insufficient evidence to conclude that the population mean price at this dealership differs from the national mean price of 10,191.

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 10,191.

Answer 1

The statistical software output for this problem is:

On the basis of above output:

a) Hypotheses:

H₀: μ = 10,191

H_a: μ ≠ 10,191

b) Test statistic = -2.227

c) P - value = 0.0305

Conclusion: Reject H₀. There is sufficient evidence to conclude that the population mean price at this dealership differs from the national mean price of 10,191.