EBK STATISTICS FOR BUSINESS & ECONOMICS
12th Edition
ISBN: 9780100460461
Author: Anderson
Publisher: YUZU
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Chapter 16, Problem 2CP
Rating Wines from the Piedmont Region of Italy
Wine Spectator magazine contains articles and reviews on every aspect of the wine industry, including ratings of wine from around the world. In a recent issue they reviewed and scored 475 wines from the Piedmont region of Italy using a 100-point scale (Wine Spectator, April 30, 2011). The following table shows how the Wine Spectator score each wine received is used to rate each wine as being classic, outstanding, very good, good, mediocre, or not recommended.
| Score | Rating |
| 95–100 | Classic: a great wine |
| 90–94 | Outstanding: a wine of superior character and style |
| 85–89 | Very good: a wine with special qualities |
| 80–84 | Good: a solid, well-made wine |
| 75–79 | Mediocre: a drinkable wine that may have minor flaws |
| below 75 | Not Recommended |
A key question for most consumers is whether paying more for a bottle of wine will result in a better wine. To investigate this question for wines from the Piedmont region we selected a random sample of 100 of the 475 wines that Wine Spectator reviewed. The data, contained in the file named WineRatings, shows the price ($), the Wine Spectator score, and the rating for each wine.
Managerial Report
- 1. Develop a table that shows the number of wines that were classified as classic, outstanding, very good, good, mediocre, and not recommended and the average price. Does there appear to be any relationship between the price of the wine and the Wine Spectator rating? Are there any other aspects of your initial summary of the data that stand out?
- 2. Develop a
scatter diagram with price on the horizontal axis and the Wine Spectator score on the vertical axis. Does the relationship between price and score appear to be linear? - 3. Using linear regression, develop an estimated regression equation that can be used to predict the score given the price of the wine.
- 4. Using a second-order model, develop an estimated regression equation that can be used to predict the score given the price of the wine.
- 5. Compare the results from fitting a linear model and fitting a second-order model.
- 6. As an alternative to fitting a second-order model, fit a model using the natural logarithm of price as the independent variable. Compare the results with the second-order model.
- 7. Based upon your analysis, would you say that spending more for a bottle of wine will provide a better wine?
- 8. Suppose that you want to spend a maximum of $30 for a bottle of wine. In this case, will spending closer to your upper limit for price result in a better wine than a much lower price?
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1- Let A = {A1, A2, ...), in which A, A, = 0, when i j.
a) Is A a π-system? If not, which element(s) should be added to A to become a π-system?
b) Prove that σ(A) consists of the finite or countable unions of elements of A; i.c., A E σ(A) if and
only if there exists finite or countable sequence {n} such that A = U₁An (Hint: Let F be such
class; prove that F is a σ-filed containing A.)
c) Let p ≥ 0 be a sequence of non-negative real numbers with Σip₁ = 1. Using p₁'s, how do you
construct a probability measure on σ(A)? (Hint: use extension theorem.)
2- Construct an example for which P(lim sup A,) = 1 and P(lim inf An) = 0.
In a town with 5000 adults, a sample of 50 is selected using SRSWOR and asked their opinion of a proposed municipal project; 30 are found to favor it and 20 oppose it. If, in fact, the adults of the town were equally divided on the proposal, what would be the probability of observing what has been observed? Approximate using the Binomial distribution. Compare this with the exact probability which is 0.0418.
Chapter 16 Solutions
EBK STATISTICS FOR BUSINESS & ECONOMICS
Ch. 16.1 - Consider the following data for two variables, x...Ch. 16.1 - Consider the following data for two variables, x...Ch. 16.1 - Prob. 3ECh. 16.1 - A highway department is studying the relationship...Ch. 16.1 - In working further with the problem of exercise 4,...Ch. 16.1 - A study of emergency service facilities...Ch. 16.1 - In 2011, home prices and mortgage rates fell so...Ch. 16.1 - Corvette, Ferrari, and Jaguar produced a variety...Ch. 16.1 - Kiplingers Personal Finance Magazine rated 359...Ch. 16.2 - In a regression analysis involving 27...
Ch. 16.2 - In a regression analysis involving 30...Ch. 16.2 - The Ladies Professional Golfers Association (LPGA)...Ch. 16.2 - Refer to exercise 12. a. Develop an estimated...Ch. 16.2 - A 10-year study conducted by the American Heart...Ch. 16.2 - In baseball, an earned run is any run that the...Ch. 16.4 - A study provided data on variables that may be...Ch. 16.4 - The Ladies Professional Golfers Association (LPGA)...Ch. 16.4 - Jeff Sagarin has been providing sports ratings for...Ch. 16.4 - Prob. 19ECh. 16.5 - Consider a completely randomized design involving...Ch. 16.5 - Prob. 21ECh. 16.5 - Prob. 22ECh. 16.5 - The Jacobs Chemical Company wants to estimate the...Ch. 16.5 - Four different paints are advertised as having the...Ch. 16.5 - An automobile dealer conducted a test to determine...Ch. 16.5 - A mail-order catalog firm designed a factorial...Ch. 16.6 - The following data show the daily closing prices...Ch. 16.6 - Refer to the Cravens data set in Table 16.5. In...Ch. 16 - A sample containing years to maturity and yield...Ch. 16 - Consumer Reports tested 19 different brands and...Ch. 16 - A study investigated the relationship between...Ch. 16 - Refer to the data in exercise 31. Consider a model...Ch. 16 - Refer to the data in exercise 31. a. Develop an...Ch. 16 - Prob. 34SECh. 16 - Rating Wines from the Piedmont Region of Italy...
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