Statistical investigation and everyday statistics

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Statistical investigation:
Your Econ 3100 classmate Kim would like to buy a used Volkswagon Eurovan for an extended
road trip this summer. Her neighbor Tim has offered to sell her his Eurovan. Tim?s Eurovan is
has 75,000 miles on it. Kim and Tim agree that the van is in average condition. Tim has asked
her to come up with a fair price. Your classmate has never heard of ?blue book value? and sets
out to estimate the value using her newly acquired knowledge of regression analysis. She checks
the Seattle Times and finds a long list of Eurovans for sale. She selects a random sample of 10 vans,
ranging in mileage from 59,000 to 129,000 miles. For each Eurovan, she enters the mileage (in 1000s)
and the offered sales price (in $1000s) into JMP. She runs a regression predicting asking price in
thousands based on mileage in thousands. She determines the relationship between mileage and
asking price and also runs some estimates for the price of a Eurovan with 75,000 miles on it.
1. What is the estimated regression equation?
2. To what extent is variation in the prices of the vans explained by differences in their mileage?
3. Give a 95% confidence interval for the coefficient on mileage.
4. Interpret the confidence interval calculated in question 3. Exactly what does it tell you?
5. Sketch a graph illustrating the estimated relationship between mileage and a van?s price.
6. Give a point estimate of the predicted price for a Eurovan in average condition with 75,000
miles on it.
7. Give a 95% confidence interval for the average price of Eurovans with 75,000 miles on them.
8. Give a 95% confidence interval (prediction interval) for the price of an individual Eurovan
with 75,000 miles on it.
9. Explain carefully why the confidence interval you gave for the individual van is wider that
that you gave for the average van.
10. Assuming that your classmate and Tim agree that his van is in average condition, what price
should she offer him? What is the price you would consider fair? Explain.
11. The sample contains a Eurovan with 81,718 thousand miles on it. Assuming that the price
given accurately reflects the condition of the car, do you think this van is likely to be in belowaverage, average, or above average condition, given its mileage? Explain your answer.
12. Does the residual plot give any suggestion that one of the assumptions of the regression
model may be violated? If not, why not? If so, which of the assumptions may be violated, and
what in the residual plot indicates this.
13. Conduct a t-test at a 0.05 significance level as to whether mileage has a statistically
significant relationship to the price of a van. Be sure to provide the hypotheses, test statistics, pvalue and conclusion. Summarize the test result in a non-technical sentence.
14. Now suppose a researcher wanted to provide evidence using a 0.05 significance level, that
the price of a van declines by more than $250 for each additional 1,000 on the odometer. What
would be the appropriate hypotheses? The test statistic? The p-value? The conclusion?
Everyday statistics
Please read the article ?Scientific Method: Statistical Errors.? You can find it online at:
1. What is the definition of ?p-value? given in the article?
2. According to the article, how did the p-value come into widespread use in scientific research?
3. The article mentions a study of online dating. What were the statistically significant findings
of that study?
4. Again, referring to the study of online dating mentioned in the article, to what extent were the
findings reported substantially significant? That is, how large were the differences described
between couples who met online and couples who did not?
5. The article describes a phenomenon called ?p-hacking,? whereby researchers manipulate their
studies in order to reduce the p-values and produce statistically significant findings. List some of
the ways that researchers might manipulate their results in order to produce statistically
significant findings (low p-values).
6. What are some ways that researchers might go about improving their research, that is, what
might they do beyond just using p-values to establish the validity of their findings?

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