Option #1: Critical Thinking: Cars

Option #1: Critical Thinking: Cars

An expert who works for a car magazine obtained random data (rounded to the nearest thousand) among two categories of used or new cars: Domestic Foreign

The expert would like to understand sales based on list price (rounded to the nearest thousand dollars), sale price (rounded to the nearest thousand dollars), and number of days it takes to sell each car. The complete data set is in the file named Cars.

Managerial Report

Prepare a report (see below) that summarizes your assessment of the nature of the car market. Be sure to include the following seven items in your report.

  1. Calculate descriptive statistics (mean, median, range, standard deviation, and coefficient of variation) to summarize each of the three variables for the all Domestic cars.
    • Use z-scores to determine if there any outliers in the data set for any of the three variables. If there are any outliers in any category, please list them and state for which category they are an outlier.
    • If a result is an outlier, state whether it is below or above the mean.
    • How can one use the above descriptive statistics to understand the Domestic car market better?
    • Could there be any other descriptive statistics that can help one understand the Domestic car market better?
  2. Descriptive statistics (mean, median, range, standard deviation, and coefficient of variation) to summarize each of the three variables for the all Foreign cars.
    • Use z-scores to determine if there any outliers in the data set for any of the three variables.
    • If there are any outliers in any category, please list them and state for which category they are an outlier.
    • If a result is an outlier, state whether it is below or above the mean.
    • How can one use the above descriptive statistics to understand the Foreign car market better?
    • Could there be any other descriptive statistic that can help one understand the Foreign car market better?
  3. Compare your summary results from #1 and #2. Discuss any specific statistical results that would help the car expert understand the two-car markets.
  4. Develop a 98% confidence interval estimate of the population mean sales price and population mean number of days to sell for Domestic cars. What is the margin of error?
    • Interpret what each confidence intervals means. How can both confidence intervals provide useful car sales information?
    • What other confidence interval would you choose to compute to obtain more information related to Domestic car sales? Explain why.
    • What happens to the confidence interval as the level of confidence is increased?
  5. Develop a 98% confidence interval estimate of the population mean sales price and population mean number of days to sell for Foreign cars. What is the margin of error?
    • Interpret what each confidence intervals means. How can both confidence intervals provide useful car sales information?
    • What other confidence interval would you choose to compute to obtain more information related to Domestic car sales? Explain why.
  6. Assume the car expert requested estimates of the mean number of days to sell for the Domestic cars with a margin of error of seven days and the mean selling price of foreign cars with a margin of error of eight days.
    • Using 98% confidence, how large should the sample sizes be for each one?
    • How could the sample size formula be useful in understanding both types of car businesses? What are some advantages of a larger sample size?
    • Suppose a Domestic car has a list price of $30,000 and a Foreign car has a list price of $30,000. What is your estimate of the final selling price (based on the percent difference for the sale and list price) and number of days required to sell each of these cars?
    • How would these two estimates be useful in this application?
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