dolution

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CASE

THE NEW ZEALAND WINE INDUSTRY

The wine industry in New Zealand is growing strongly. In 2009 (to year end June), total sales of New Zealand wines were a staggering 172 million litres, the highest the industry has ever seen. The same year witnessed the opening of the 640th winery. Export sales of 112 million litres accounted for over 65% of total sales for the first time ever. However, the industry has not been without its challenges. A strong New Zealand dollar, rising costs, difficult market conditions, and economic uncertainty have all taken their toll. Notwithstanding these current problems, according to the Wine Institute of New Zealand’s New Zealand Winegrowers Annual Report, 2009, the future is bright with expectations of continued growth in sales in the foreseeable years.

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Diversity and pH The following data represent the number of fish species living in various Andirondack Lakes and the pH of the lakes. From chemistry, we know pH is a measure of the acidity or basicity of a solution. Solutions with pH less than 7 are said to be acidic. As pH increases, the solution is said to be less acidic.

(a) Draw a scatter diagram of the data treating pH as the explanatory variable.

(b) Determine the linear correlation coefficient between pH and number of fish species.

(c) Does a linear relation exist between pH and number of fish species?

(d) Find the least-squares regression line treating pH as the explanatory variable.

(e) Interpret the slope.

(f) Is it reasonable to interpret the intercept? Explain.

(g) What proportion of the variability in number of fish species is explained by pH?

(h) Is the number of fish species in the lake whose pH is 5.5 above or below average? Explain.

(i) In part (g), you found the proportion of variability in number of fish species that is explained by the variability in pH. Can you think of other variables that might also explain the variability in the number of fish species?

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Soybean Yield The data in the table represent the number of pods on a random sample of soybean plants for various plot types. An agricultural researcher wants to determine if the mean numbers of pods for each plot type are equal.

(a) Write the null and alternative hypotheses.

(b) State the requirements that must be satisfied to use the oneway ANOVA procedure.

(c) Use the following Minitab output to test the hypothesis of equal means at the  level of significance.

(d) Shown are side-by-side boxplots of each type of plot. Do these boxplots support the results obtained in part (c)?

(e) Verify that the -test statistic is 3.77.

(f) Verify the residuals are normally distributed.

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Determine the SSE and the   for Problem 12.20. Comment on the size of  for this regression model, which is used to predict the cost of Bordeaux wine.

Problem 12.20

Bordeaux is an important wine-producing region of France. Bordeaux wine is made by more than 8,500 producers or  spread over more than 1,000 square kilometres. Some people might argue that because of transportation costs, the cost of wine increases with the distance of markets from the city of Bordeaux. Suppose the wine prices in eight towns are as follows.

Use the prices along with the distance of each town from Bordeaux to develop a regression line to predict the price of a bottle of wine by the number of kilometres the town is from Bordeaux. Use the data and the regression equation to compute residuals for this model. Sketch a graph of the residuals in the order of the x values. Comment on the shape of the residual graph.

 

 

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