9.4 In an analysis of variance comparing the output of five plants, data sets of 21 observations per plant are analyzed. The computed F statistic value is 3.6. Do you believe that there are differences in average output among the five plants? What is the approximate p -value? Explain.

9.12 What is the main principle behind analysis of variance?

9.16 Does the quantity MSTR/MSE follow an F distribution when the null hypothesis of ANOVA is false? Explain.

9.20 The manager of a store wants to decide what kind of hand-knit sweaters to sell. The manager is considering three kinds of sweaters: Irish, Peruvian, and Shetland. The decision will depend on the results of an analysis of which kind of sweater, if any, lasts the longest before wearing out. The manager has some data collected from various customers who in the past bought different sweaters and reported how many years their sweaters lasted before wearing out. There are 20 observations on Irish sweaters, 18 on Peruvian sweaters, and 21 on Shetland sweaters. The data are assumed to be independent random samples from the three populations of sweaters. The manager hires a statistician, who carries out an ANOVA and finds SSE = 1,240 and SSTR = 740. Construct a complete ANOVA table, and determine whether there is evidence to conclude that the three kinds of sweaters do not have equal average durability.

10.4 Define the parameters of the simple linear regression model.

10.6 What are the uses of a regression model?

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10.10 (A conceptually advanced problem) Can you think of a possible limitation of the least-squares procedure?

10.14 A pharmaceutical manufacturer wants to determine the concentration of a key component of cough medicine that may be used without the drug’s causing adverse side effects. As part of the analysis, a random sample of 45 patients is administered doses of varying concentrations ( X ), and the severity of side effects ( Y ) is measured. The results include \(\overline{x}\) = 88.9, \(\overline{y}\) = 165.3, \(\) SS x = 2,133.9, SS xy = 4,502.53, SS y = 12,500. Find the least squares estimates of the regression parameters.

10.22 Give 95% confidence intervals for the regression slope and the regression intercept parameters for the situation of problem 10-11.

Problem 10-11: Run a regression analysis of the data in the table and determine the linear relationship between energy density and total number of calories. Take energy density as the independent variable.

Food Energy Density Total Calories

1 Jelly Doughnut 3.4 289

2 Frozen Waffles 2.5 191

1 Flour Tortilla 3.3 114

2 Corn Tortillas 2.2 112

½ Cup Granola 4.6 220

1 Cup Oatmeal 0.6 145

¼ Cup Raisins 3.0 109

1 ½ Cup Grapes 0.7 92

M&M Plain 4.9 236

2 Cream-filled

Chocolate Cupcakes 3.6 230

4oz. Margarita 2.2 271

4oz. White Wine 0.7 80

1 Cup Cheese Ravioli 3.2 280

1 Slice Thick-crust

Cheese Pizza 2.9 202

2 Reese’s Peanut

Butter Cups 5.4 271

1 Slice Frosted

Chocolate Cake 3.7 235

1 Cup Cream of

Broccoli/Cheese Soup 0.8 190

1 Cup Chicken Noodle

Soup 0.3 75

1 Cup Premium Ice

Cream 2.6 540

12 oz. Hardee’s

Vanilla Shake 1.0 350

8 oz. Eggnog 1.4 342

8 oz. Hot Cocoa 0.5 124

1 Hotdog w/Bun 2.5 242

1 Cup Beef Stew w/

Vegetables 0.9 220

10.48 What is \({{r}^{2}}\) in the regression of problem 10-13?

Problem 10-13: Recently, research efforts have focused on the problem of predicting a manufacturer’s market share by using information on the quality of its product. Suppose that the following data are available on market share, in percentage ( Y ), and product quality, on a scale of 0 to 100, determined by an objective evaluation procedure ( X ).:

X: 27 39 73 66 33 43 47 55 60 68 70 75 83

Y: 2 3 10 9 4 6 5 8 7 9 10 13 12

10.28 Compute the sample correlation coefficient for the data of problem 10-13.

(See above problem for data from 10-13).

1. A study was conducted to determine whether a correlation exists between consumers’ perceptions of a television commercial (measured on a special scale) and their interest in purchasing the product (measured on a scale). The results are n = 65 and r = 0.37. Is there statistical evidence of a linear correlation between the two variables?

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