A magazine collected the ratings for food, decor, service and the cost per person for a sample of 102 restaurants. They combined the ratings to create a summated rating and used that to predict the cost of a restaurant meal. The data are modeled by Y₁ = -25.002+1.0004X₁, where X; is summated ratings and Ŷ¡ is meal cost. For these data, Syx = 8.731, X = 62.59, and h; = 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=X₁ ≤ 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. 0.004sYx=545 (Type integers or decimals. Round to three decimal places as needed. Use ascending order.) S
A magazine collected the ratings for food, decor, service and the cost per person for a sample of 102 restaurants. They combined the ratings to create a summated rating and used that to predict the cost of a restaurant meal. The data are modeled by Y₁ = -25.002+1.0004X₁, where X; is summated ratings and Ŷ¡ is meal cost. For these data, Syx = 8.731, X = 62.59, and h; = 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=X₁ ≤ 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. 0.004sYx=545 (Type integers or decimals. Round to three decimal places as needed. Use ascending order.) S
Transcribed Image Text:A magazine collected the ratings for food, decor, service and the cost per person for a sample of 102 restaurants. They combined the ratings to
create a summated rating and used that to predict the cost of a restaurant meal. The data are modeled by Y = -25.002 + 1.0004X;, where X; is t
summated ratings and Ỹ; 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=Xi
(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.
0.004 ≤Yx
≤ 31.40
X = 54
(Type integers or decimals. Round to three decimal places as needed. Use ascending order.)
