10.6 Tuna Fish Is there a difference in the prices of tuna, depending on the method of packaging? Consumer Reports gives the estimated average price for a 170-gram (g) can or a 200-gram pouch of tuna, based on prices paid nationally in supermarkets. These prices are recorded for a variety of different brands of tuna.

Assume that the tuna brands included in this survey represent a random sample of all tuna brands available in North America.

a. Find a 95% confidence interval for the average price for light tuna in water. Interpret this interval. That is, what does the "95%" refer to?

b. Find a 95% confidence interval for the average price for white tuna in oil. How does the width of this interval compare to the width of the interval in part a? Can you explain why?

c. Find 95% confidence intervals for the other two sam- ples (white tuna in water and light tuna in oil). Plot the four treatment means and their standard errors in a two-dimensional plot similar to Figure 8.5. What kind of broad comparisons can you make about the four treatments? (We will discuss the procedure for comparing more than two population means in Chapter 11.)

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Light Tuna in Water White Tuna in Oil White Tuna in Water Light Tuna in Oil 0.99 0.53 1.27 1.49 2.56 0.62 1.92 1.41 1.22 1.29 1.92 0.66 1.23 1.12 1.19 1.27 1.30 0.62 0.85 0.63 1.22 1.35 1.79 0.65 0.65 0.67 1.29 1.23 0.60 0.69 0.60 1.00 0.67 0.60 0.66 1.27 1.28 Source: "Tuna Goes Upscale" 2001, Consumers Union of U.S., Inc. Yonkers, NY 10703-1057, a nonprofit organization. Reprinted with permission from the June 2001 Issue, of Consumer Reports for educational purposes only.