13. (20 pts) A consumer organization was concerned that an automobile manufacturer was misleading customers by overstati

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13 20 Pts A Consumer Organization Was Concerned That An Automobile Manufacturer Was Misleading Customers By Overstati 1 (99.3 KiB) Viewed 70 times

13. (20 pts) A consumer organization was concerned that an automobile manufacturer was misleading customers by overstating the average fuel efficiency (measured in miles per gallon, or mpg) of a particular car model. The model was advertised to get 27 mpg. To investigate, researchers selected a random sample of 10 cars of that model. Each car was then randomly assigned a different driver. Each car was driven for 5,000 miles, and the total fuel consumption was used to compute mpg for that car. (a) Define the parameter of interest and ... state the null and alternative hypotheses the consumer organization is interested in testing. One condition for conducting a one-sample t-test in this situation is that the mpg measurements for the population of cars of this model should be normally distributed. However, the boxplot and histogram shown below indicate that the distribution of the 10 sample values is skewed to the right. Number of Cars 23 33 Miles per Gallon (b) One possible statistic that measures skewness is the ratio sample mean/sample median. What values of that statistic (small, large, close to one) might indicate that the population distribution of mpg values is skewed to the right? Explain. C) Even though the mpg values in the sample were skewed to the right, it is still possible that the population distribution of mpg values is normally distributed and that the skewness was due to sampling variability. To investigate, 100 samples, cach of size 10, were taken from a normal distribution with the same mean and standard deviation as the original sample. For each of those 100 samples, the statistic sample mean/sample median was calculated. A dotplot of the 100 simulated statistics is shown below. 0.94 0.95 0.96 0.97 0.98 0.99 1.00 1.01 1.02 103 104 105 1.06 sample mean/sample median In the original sample, the value of the statistic sample mean/sample median was 1.03. Based on the value of 1.03 and the dotplot above, is it plausible that the original sample of 10 cars came from a normal population, or do the simulated results suggest the original population is really skewed to the right? Explain. (d) The table below shows summary statistics for mpg measurements for the original sample of 10 cars. Minimum 01 Median 03 Maximum 23 24 25.5 28 32 Choosing only from the summary statistics in the table, define a formula for a different statistic that measures skewness. What values of that statistic might indicate that the distribution is skewed to the right? Explain.