A magazine collected the ratings for food, decor, service and the cost per person for a sample of 102 restaurants. They combined the ratings tocreate a summated rating and used that to predict the cost of a restaurant meal. The data are modeled by Ỹ; = -25.002 + 1.0004X₁, where X¡ issummated ratings and Ŷ¡ is meal cost. For these data, Syx = 8.731, X = 62.59, and h₁ = 0.026985 when X= 54. Complete parts (a) through (c).a. Construct a 90% confidence interval estimate of the mean cost of a meal for restaurants that have a summated rating of 54.26.639 HY|X=Xj<31.40(Type integers or decimals. Round to three decimal places as needed. Use ascending order.)b. Construct a 90% prediction interval of the cost of a meal for an individual restaurant that has a summated rating of 54.14.33 ≤Yx=54 ≤ 43.709s(Type integers or decimals. Round to three decimal places as needed. Use ascending order.)c. Explain the differences in the results from (a) and (b). Choose the correct answer below.O A. Since there is more variation in estimating a mean value than in predicting an individual value, the confidence interval is wider than theprediction interval, holding everything else fixed.B. Since there is more variation in predicting an individual value than in estimating a mean value, the prediction interval is narrower than thconfidence interval, holding everything else fixed. c. Explain the differences in the results from (a) and (b). Choose the correct answer below.O A. Since there is more variation in estimating a mean value than in predicting an individual value, the confidence interval is wider than theprediction interval, holding everything else fixed.B. Since there is more variation in predicting an individual value than in estimating a mean value, the prediction interval is narrower than theconfidence interval, holding everything else fixed.OC. Since there is more variation in predicting an individual value than in estimating a mean value, the prediction interval is wider than theconfidence interval, holding everything else fixed.D. Since there is more variation in estimating a mean value than in predicting an individual value, the confidence interval is narrower than theprediction interval, holding everything else fixed.

Confidence intervals and prediction intervals are two interval that are frequently used in…

A magazine collected the ratings for food, decor, service and the cost per person for a sample of 102 restaurants. They combined the rating create a summated rating and used that to predict the cost of a restaurant meal. The data are modeled by Y₁ = = -25.002+1.0004X;, where summated ratings and Ỹ; is meal cost. For these data, Syx = 8.731, X=62.59, and h; = 0.026985 when X = 54. Complete parts (a) through a. Construct a 90% confidence interval estimate of the mean cost of a meal for restaurants that have a summated rating of 54. 26.639 SHY|X=x; $ 31.40 (Type integers or decimals. Round to three decimal places as needed. Use ascending order.) b. Construct a 90% prediction interval of the cost of a meal for an individual restaurant that has a summated rating of 54. 14.33 ≤Yx=54 ≤ 43.709 (= (Type integers or decimals. Round to three decimal places as needed. Use ascending order.) c. Explain the differences in the results from (a) and (b). Choose the correct answer below.