A movie studio wishes to determine the relationship between the revenue from the rental of comedies on DVD and videotape and the revenue generated fromthe theatrical release of such movies. The studio has bivariate data from a sample of 13 comedies released over the past five years. These data give the revenuex from theatrical release (in millions of dollars) and the revenue y from DVD and videotape rentals (in millions of dollars) for each of the 13 movies. The least-squares regression equation computed from the data is y= 3.57+0.13x.The studio has plans for the DVD/video release of a comedy that grossed about 40.5 million dollars in theaters. The studio has predicted the rental revenue fromthis release using the regression equation and is now interested in both a prediction interval for this rental revenue and a confidence interval for the mean rentalrevenue of movies generating this same theater revenue. The studio has already computed the following for their data:• mean square error (MSE) ~ 14.65;2(40.5 – x,1+13- 0.0977,132ΣX;i = 1where x1, X2'denote the theater revenues in the sample, and x denotes their mean.... *13Based on this information, and assuming that the regression assumptions hold, answer the questions in the table below.Lower limit:1. What is the 90% confidence interval for the mean rental revenue (in millions of dollars) when thetheater revenue is 40.5 million dollars? (Carry your intermediate computations to at least four decimalplaces, and round your answer to at least one decimal place.)Upper limit:2. Choose one response to answer the question below.Consider (but do not actually compute) the 90% prediction interval for an individual value for rental revenue when the theaterrevenue is 40.5 million dollars. How would the confidence interval computed above compare to this prediction interval (assumingthat both intervals are computed from the same sample data)? 132Σ(+;- )i= 1where x1, X2:, x13 denote the theater revenues in the sample, and x denotes their mean..../Based on this information, and assuming that the regression assumptions hold, answer the questions in the table below.Lower limit:1. What is the 90% confidence interval for the mean rental revenue (in millions of dollars) when thetheater revenue is 40.5 million dollars? (Carry your intermediate computations to at least four decimalplaces, and round your answer to at least one decimal place.)Upper limit:2. Choose one response to answer the question below.Consider (but do not actually compute) the 90% prediction interval for an individual value for rental revenue when the theaterrevenue is 40.5 million dollars. How would the confidence interval computed above compare to this prediction interval (assumingthat both intervals are computed from the same sample data)?Choose one3. Choose one response to answer the question below.For the theater revenue values in this sample, 23.3 million dollars is more extreme than 40.5 million dollars is, that is, 23.3 isfarther from the sample mean theater revenue than 40.5 is. How would the 90% confidence interval for the mean rental revenuewhen the theater revenue is 23.3 million dollars compare to the 90% confidence interval for the mean rental revenue when thetheater revenue is 40.5 million dollars?Choose one?13

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