Question

9. At a certain school, 41% of the students play soccer, 30% play volleyball, and 14% play both soccer and volleyball. If a student is chosen at random, find the probability that he/she plays neither soccer nor volleyball.: *
(A) 0.71
(B) 0.57
(C) 0.43
(D) 0.413

Questions 10-12: A simple linear regression model was fit to the situation of using the number of pages in a book (in hundreds) to predict the number of typos in the book. The equation is y = 1.2 + 3.4x.

10. Interpret the slope.: *
(A) For every additional page in length, a book is expected to have an extra 3.4 typos on average.
(B) A 400-page book, on average, should have 3.4 more typos than a 300-page book.
(C) For every additional 3.4 pages in length, a book is expected to have an extra 1.2 typos on average.
(D) The slope has no practical interpretation in this context.

11. Find the predicted number of typos in a 500-page book.: *
(A) 17
(B) 18.2
(C) 171.2
(D) 1701.2

12. Explain what it would mean if an actual 500-page book had a residual of -3.2.: *
(A) This particular book is definitely an outlier and should be dropped from the model.
(B) This particular book had a predicted value smaller than its actual value.
(C) This particular book had a predicted value larger than its actual value.
(D) A mistake has been made since residuals cannot be negative.

Answer 1

9) Let S be the set containing the students who play soccer.Let V be the set containing the students who play volleyball.

Probalbility that a student plays soccer=Probability that a student belongs to the set S=P(S)=0.41

Probablity that a student plays volleyball=Probability that a student belongs to the set V=P(V)=0.30

P(SV) =P(S)+P(V)- P(S V )=0.41+0.30-0.14=0.57

Probablity that a student plays both soccer and volleyball=Probability that a student belongs to the set S V =

P(S V ) =0.14

Probaility that a student plays neither soccer nor volleyball= (P(SV))c=1- P(SV) =1-0.57=0.43 (C)

10) Since the slope indicates the increase in the y with unit increase in x, here the slope can be interpreted as in option (A).

11) From the given regression equation we can determine the number of typos when the number of pages in a book is given.

If the number of pages in a book is 500,then that means x=500. So predicted number of typos in that book is=y= 1.2+3.4 *500= 1701.2

So option D is correct.

12)The difference between the actual value of y and the predicted value of y is known as residual.

The appropriateness of a linear regression model is measured in terms of residual.An actual 500-page book had a residual of -3.2 means that this particular book had a predicted value larger than its actual value. So option C is correct.