Problem 1
A chemical reaction is run 12 times, and the temperature xi (in C) and the yield yi (in percent of a theoretical maximum) is recorded each time. The following summary statistics are recorded: x = 65.0 y = 29.05 12 i=1 (xi x) 2 = 6032.0 12 i=1 (yi y) 2 = 835.42 12 i=1 (xi x)(yi y) = 1988.4 Let 0 represent the hypothetical yield at a temperature of 0C, and let 1 represent the increase in yield caused by an increase in temperature of 1C. Assume that assumptions 1 through 4 on page 544 hold. a. Compute the least-squares estimates 0 and 1. b. Compute the error variance estimate s2 . c. Find 95% confidence intervals for 0 and 1. d. A chemical engineer claims that the yield increases by more than 0.5 for each 1C increase in temperature. Do the data provide sufficient evidence for you to conclude that this claim is false? e. Find a 95% confidence interval for the mean yield at a temperature of 40C. f. Find a 95% prediction interval for the yield of a particular reaction at a temperature of 40C. 2

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The answer to “A chemical reaction is run 12 times, and the temperature xi (in C) and the yield yi (in percent of a theoretical maximum) is recorded each time. The following summary statistics are recorded: x = 65.0 y = 29.05 12 i=1 (xi x) 2 = 6032.0 12 i=1 (yi y) 2 = 835.42 12 i=1 (xi x)(yi y) = 1988.4 Let 0 represent the hypothetical yield at a temperature of 0C, and let 1 represent the increase in yield caused by an increase in temperature of 1C. Assume that assumptions 1 through 4 on page 544 hold. a. Compute the least-squares estimates 0 and 1. b. Compute the error variance estimate s2 . c. Find 95% confidence intervals for 0 and 1. d. A chemical engineer claims that the yield increases by more than 0.5 for each 1C increase in temperature. Do the data provide sufficient evidence for you to conclude that this claim is false? e. Find a 95% confidence interval for the mean yield at a temperature of 40C. f. Find a 95% prediction interval for the yield of a particular reaction at a temperature of 40C. 2” is broken down into a number of easy to follow steps, and 190 words. Statistics for Engineers and Scientists was written by and is associated to the ISBN: 9780073401331. Since the solution to 1 from 7.3 chapter was answered, more than 342 students have viewed the full step-by-step answer. This textbook survival guide was created for the textbook: Statistics for Engineers and Scientists , edition: 4. The full step-by-step solution to problem: 1 from chapter: 7.3 was answered by , our top Statistics solution expert on 06/28/17, 11:15AM. This full solution covers the following key subjects: . This expansive textbook survival guide covers 153 chapters, and 2440 solutions.