A typing instructor builds a regression model to investigate what factors determine typing speed for students with two months of instruction. Her regression equation looks like: Y' = 7x3 + 5x2 + 3x + 11 where: Y' = typing speed in words per minute; x3 = hours of instruction per week; x2 = hours of practice per week; x = hours of typing per week necessary for school or work; A new student is taking 2 hrs of typing instruction per week, will practice 5 hrs per week and must type 2.5 hours per week for work. If the standard error of the estimate is 4, within what range do we have a 95.45% probability that that student's typing speed will be in two months? A. 53.5 and 61.5 words per minuteB. 49.5 and 65.5 words per minuteC. 57.5 and 65.5 words per minuteD. none of the above

Question

Mathematics

Tommy Best

24 February, 19:32

A typing instructor builds a regression model to investigate what factors determine typing speed for students with two months of instruction. Her regression equation looks like: Y' = 7x3 + 5x2 + 3x + 11 where: Y' = typing speed in words per minute; x3 = hours of instruction per week; x2 = hours of practice per week; x = hours of typing per week necessary for school or work; A new student is taking 2 hrs of typing instruction per week, will practice 5 hrs per week and must type 2.5 hours per week for work. If the standard error of the estimate is 4, within what range do we have a 95.45% probability that that student's typing speed will be in two months? A. 53.5 and 61.5 words per minuteB. 49.5 and 65.5 words per minuteC. 57.5 and 65.5 words per minuteD. none of the above

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Answers (1)

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Luciano Horn · Answer 1

B. 49.5 and 65.5 words per minute

Step-by-step explanation:

95.45% range estimate for the student's typing speed can be calculated using the equation Y± (z*SE) where

Y is the mean typing speed regression estimate for 2 hrs of typing instruction, 5 hrs practice and 2.5 hours work per week. (7*2 + 5*5 + 3*2.5 + 11 = 57.5 hours) z is the z-score for 95.45% probability (2) SE is the standard error of the estimate (4 hours)

Thus, Y± (z*SE) = 57.5± (2*4) that is, 95.45% probability range for the student's typing speed is between 49.5 hours and 65.5 hours