In the early 1990s researchers at The Ohio State University studied consumer ratings of six fast-food restaurants: Borden Burger, Hardee€™s, Burger King, McDonald€™s, Wendy€™s, and White Castle. Each of 406 randomly selected individuals gave each restaurant a rating of 1, 2, 3, 4, 5, or 6 on the basis of taste, and then ranked the restaurants from 1 through 6 on the basis of overall preference. In each case, 1 is the best rating and 6 the worst. The mean ratings given by the 406 individuals are given in the following table:

If we use simple linear regression to relate the dependent variable mean preference to the independent variable mean taste, we find that the least squares point estimate of β1 is b1 = 1.2731, and we find that the standard error of this point estimate is sb1 = .1025. (1) Interpret b1, and (2) find and interpret a 95 percent confidence interval for β1.

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Restaurant Borden Burger Hardee's Burger King McDonald's Wendy's White Castle Mean Taste 3.5659 3.329 2.4231 2.0895 1.9661 3.8061 Mean Preference 4.2552 4.0911 3.0052 2.2429 2.5351 4.7812