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 = -25.002 + 1.0004X;, where X; is the 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 (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. ≤YX= 54 ³ (Type integers or decimals. Round to three decimal places as needed. Use ascending order.)

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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+1.0004X₁, where X; is the
summated ratings and 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 = 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.
|≤YX=54≤
(Type integers or decimals. Round to three decimal places as needed. Use ascending order.)
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+1.0004X₁, where X; is the summated ratings and 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 = 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. |≤YX=54≤ (Type integers or decimals. Round to three decimal places as needed. Use ascending order.)
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