Answer:
The range that has a 95.45% probability that that student's typing speed will be in two months is [49.5, 65.5].
Explanation:
The compete question is:
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?
Solution:
The regression equation formed by the typing instructor to investigate what factors determine typing speed for students with two months of instruction is as follows:
Here,
<em>Y</em>' = typing speed in words per minute
<em>x</em>₁ = hours of instruction per week
<em>x</em>₂ = hours of practice per week
<em>x</em>₃ = hours of typing per week necessary for school or work
Compute the value of <em>Y</em>' for the given values of <em>x</em>₁, <em>x</em>₂ and <em>x</em>₃ as follows:
So, the typing speed of this student in words per minute is 57.5.
The range providing the (1 - <em>α</em>)% prediction interval for values of <em>Y</em>' is:
Since the data selected is for 2 months the sample size is too large.
The critical value of <em>t</em> is 2.
Compute the range as follows:
Thus, the range that has a 95.45% probability that that student's typing speed will be in two months is [49.5, 65.5].