Thirty-four customers at Starbucks either ordered coffee (C) or did not order coffee (X).

Research question: At $\alpha = .05$, is the sequence random?

$$C X C X C C C C X X X X C X C X C X C C C X C X C C X C X X X C C X$$

(a) Plot U.S. petroleum imports on a graph. (b) Describe the trend (if any) and discuss possible causes. (c) Fit both a linear and an exponential trend. (c) Interpret each fitted trend equation, explaining the implications. (d) Make a projection for 2010 . Do you believe it? (e) To whom is this issue relevant? Note: Time increments are 5 years, so use $t=11$ for the 2010 forecast.

$$\begin{aligned} &\text { U.S. Annual Petroleum Imports, 1960-2005 (billions of barrels) }\\ &\begin{array}{cccc} \hline \text { Year } & \text { Imports } & \text { Year } & \text { Imports } \\ \hline 1960 & 664 & 1985 & 1,850 \\ 1965 & 901 & 1990 & 2,926 \\ 1970 & 1,248 & 1995 & 3,225 \\ 1975 & 2,210 & 2000 & 4,194 \\ 1980 & 2,529 & 2005 & 4,937 \end{array} \end{aligned}$$

(a) Plot both men's and women's winning times on the same graph. (b) Fit a linear trend model to each series (men, women). (c) Use Excel's option to forecast each trend graphically to 2040 (i.e., to period $t=27$ periods, because observations are in 4-year increments). From these projections, does it appear that the times will eventually converge? ${ }^*(\mathrm{~d})$ Set the fitted trends equal, solve for $x$ (the time period when the trends will cross), and convert $x$ to a year. Is the result plausible? Explain. (e) Use the Web to check your 2004 and 2008 forecasts.

$$\begin{aligned} &\text { Summer Olympics 100-Meter Winning Times }\\ &\begin{array}{llclc} \hline \text { Year } & \text { Men's 100-Meter Winner } & \text { Seconds } & \text { Women's 100-Meter Winner } & {\text { Seconds }} \\ \hline 1928 & \text { Percy Williams, Canada } & 10.80 & & \text { Elizabeth Robinson, United States } \\ 1932 & \text { Eddie Tolan, United States } & 10.30 & \text { Stella Walsh, Poland } & 12.20 \\ 1936 & \text { Jesse Owens, United States } & 10.30 & \text { Helen Stephens, United States } & 11.90 \\ 1948 & \text { Harrison Dillard, United States } & 10.30 & \text { Fanny Blankers-Koen, Netherlands } & 11.50 \\ 1952 & \text { Lindy Remigino, United States } & 10.40 & \text { Marjorie Jackson, United States } & 11.90 \\ 1956 & \text { Bobby Morrow, United States } & 10.50 & \text { Betty Cuthbert, Australia } & 11.50 \\ 1960 & \text { Armin Hary, West Germany } & 10.20 & \text { Wilma Rudolph, United States } & 11.50 \\ 1964 & \text { Bob Hayes, United States } & 10.00 & \text { Wyomia Tyus, United States } & 11.00 \\ 1968 & \text { Jim Hines, United States } & 9.95 & \text { Wyomia Tyus, United States } & 11.40 \\ 1972 & \text { Valery Borzov, USSR } & 10.14 & \text { Renate Stecher, East Germany } & 11.00 \\ 1976 & \text { Hasely Crawford, Trinidad } & 10.06 & \text { Annegret Richter, West Germany } \\ 1980 & \text { Allan Wells, Great Britain } & 10.25 & \text { Lyudmila Kondratyeva, USSR } & 11.07 \\ 1984 & \text { Carl Lewis, United States } & 9.99 & \text { Evelyn Ashford, United States } \\ 1988 & \text { Carl Lewis, United States } & 9.92 & \text { Florence Griffith-Joyner, United States } \\ 1992 & \text { Linford Christie, Great Britain } & 9.96 & \text { Gail Devers, United States } \\ 1996 & \text { Donovan Bailey, Canada } & 9.84 & \text { Gail Devers, United States } & 11.08 \\ 2000 & \text { Maurice Greene, United States } & 9.87 & \text { Marion Jones, United States } \end{array} \end{aligned}$$

(a) Plot the data on lightning deaths.

(b) Describe the trend (if any) and discuss possible causes.

(c) Fit an exponential trend to the data. Interpret the fitted equation.

(d) Make a forecast for 2015, using a trend model of your choice (or a judgment forecast). Explain the basis for your forecast.

Note: Time is in 5-year increments, so use $t$ = 16 for your 2015 forecast.

Rates of return on 24 mutual funds are shown.

(a) Convert the data to ranks. Check the column sums.

(b) Calculate Spearman’s rank correlation coefficient. Show your calculations.

(c) At $\alpha = .01$ can you reject the hypothesis of zero rank correlation?

(d) Check your work by using MegaStat.

(e) Calculate the Pearson correlation coefficient (using Excel).

(f) In this case, why might either test be used?

Profits of 20 consumer food companies are shown.

(a) Convert the data to ranks. Check the column sums.

(b) Calculate Spearman’s rank correlation coefficient. Show your calculations.

(c) At $\alpha = .01$ can you reject the hypothesis of zero rank correlation?

(d) Check your work by using MegaStat.

(e) Calculate the Pearson correlation coefficient (using Excel).

(f) Why might the rank correlation be preferred?

JavaMax is a neighborhood take-out coffee shop that offers three sizes. Yesterday’s sales are shown. Use MegaStat or another software package to perform a Friedman test to see whether the median sales of coffee sizes differ at $\alpha = .05$, using time of day as the blocking factor.

Perform the regression and write the estimated regression equation (round off to 3 or 4 significant digits for clarity). Do the coefficient signs agree with your $a$ priori expectations?

State your a priori hypotheses about the sign ( $+$ or $-)$ of each predictor and your reasoning about cause and effect. Would the intercept have meaning in this problem? Explain.

When might a bivariate correlation be misleading?

Why is a significant correlation not proof of causation?

Consumers are asked to rate the attractiveness of four potential dashboard surface textures on an interval scale (1 = least attractive, 10 = most attractive). Use MegaStat or another software package to perform a Friedman test to see whether the median ratings of surfaces differ at $\alpha = .05$, using age as the blocking factor.

Describe the way in which ranks are assigned in calculating the Spearman rank correlation test.

hat is the purpose of the Spearman rank correlation test?