Related questions with answers

The Buyer’s Guide section of the Web site for Car and Driver magazine provides reviews and road tests for cars, trucks, SUVs, and vans. The average ratings of overall quality, vehicle styling, braking, handling, fuel economy, interior comfort, acceleration, dependability, fit and finish, transmission, and ride are summarized for each vehicle using a scale ranging from 1 (worst) to 10 (best). A portion of the data for 14 Sports/GT cars is shown here (Car and Driver website, January 7, 2004).

Sports/GTOverallHandlingDependabilityFit and FinishAcura 3.2CL7.807.838.177.67Acura RSX9.029.469.358.97Audi TT9.009.588.749.38BMW 3-Series/M38.399.528.398.55Chevrolet Corvette8.829.648.547.87Ford Mustang8.348.858.707.34Honda Civic Si8.929.319.507.93Infiniti G358.709.348.968.07Mazda RX-88.589.798.968.12Mini Cooper8.7610.008.698.33Mitsubishi Eclipse8.178.958.257.36Nissan 350Z8.079.357.568.21Porsche 9119.559.918.869.55Toyota Celica8.779.299.047.97\begin{matrix} \text{Sports/GT} & \text{Overall} & \text{Handling} & \text{Dependability} & \text{Fit and Finish}\\ \text{Acura 3.2CL} & \text{7.80} & \text{7.83} & \text{8.17} & \text{7.67}\\ \text{Acura RSX} & \text{9.02} & \text{9.46} & \text{9.35} & \text{8.97}\\ \text{Audi TT} & \text{9.00} & \text{9.58} & \text{8.74} & \text{9.38}\\ \text{BMW 3-Series/M3} & \text{8.39} & \text{9.52} & \text{8.39} & \text{8.55}\\ \text{Chevrolet Corvette} & \text{8.82} & \text{9.64} & \text{8.54} & \text{7.87}\\ \text{Ford Mustang} & \text{8.34} & \text{8.85} & \text{8.70} & \text{7.34}\\ \text{Honda Civic Si} & \text{8.92} & \text{9.31} & \text{9.50} & \text{7.93}\\ \text{Infiniti G35} & \text{8.70} & \text{9.34} & \text{8.96} & \text{8.07}\\ \text{Mazda RX-8} & \text{8.58} & \text{9.79} & \text{8.96} & \text{8.12}\\ \text{Mini Cooper} & \text{8.76} & \text{10.00} & \text{8.69} & \text{8.33}\\ \text{Mitsubishi Eclipse} & \text{8.17} & \text{8.95} & \text{8.25} & \text{7.36}\\ \text{Nissan 350Z} & \text{8.07} & \text{9.35} & \text{7.56} & \text{8.21}\\ \text{Porsche 911} & \text{9.55} & \text{9.91} & \text{8.86} & \text{9.55}\\ \text{Toyota Celica} & \text{8.77} & \text{9.29} & \text{9.04} & \text{7.97}\\ \end{matrix}

Another Sports/GT car rated by Car and Driver is the Honda Accord. The ratings for handling, dependability, and fit and finish for the Honda Accord were 8.28, 9.06, and 8.07, respectively. Estimate the overall rating for this car.

Question

In May 20082008, CNN reported that sports utility vehicles (SUVs) are plunging toward the "endangered" list. Due to the uncertainty of oil prices and environmental concerns, consumers are replacing gas-guzzling vehicles with fuel-efficient smaller cars. As a result, there has been a big drop in the demand for new as well as used SUVs. A sales manager of a used car dealership for SUVs believes that it takes more than 9090 days, on average, to sell an SUV. In order to test his claim, he samples 4040 recently sold SUVs and finds that it took an average of 95 days to sell an SUV. He believes that the population standard deviation is fairly stable at 2020 days.

b. What is the p-value?

Solution

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Considering this task we know that hypotheses look like this:

H0:μ90HA:μ>90\begin{aligned} H_0&:\mu\leq90\\ H_A&:\mu>90 \end{aligned}

and a sample of n=40n = 40 recently sold SUVs while selling one takes on average x=95\overline {x} = 95 days, while population standard deviation equals σ=20\sigma = 20. Do we need to calculate the value of the test statistic and pp- value?

Is the distribution from which the sample was isolated normal, and what test statistics can we use to our advantage?

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