1. The scatter plot below shows the relationship between pre-test and post-test scores in a...

Question

1. The scatter plot below shows the relationship between pre-test and post-test scores in a Statistics class. The horizontal axis represents the pre-test scores. Use this graph to answer the questions below.

(A) How would you describe the relationship between pre-test and post-test scores in this class?
(B) Approximately what post-test score did the student with a pre-test score of 70 receive?
(C) Would the slope of the "line of best fit" be positive or negative?
(Points : 6)
2. Suppose we want to determine the (binomial) probability(p) of getting 4 heads in 15 flips of a 2-sided coin. Using the Binomial Probabilities Table in Appendix B of the text, what values of n, x and p would we use to look up this probability, and what would be the probability?
(Points : 3)

3. For the table that follows, answer the following questions:

x	y
1	-3
2	-2
3	-1
4

- Would the correlation between x and y in the table above be positive or negative?
- Find the missing value of y in the table.
- How would the values of this table be interpreted in terms of linear regression?
- If a "line of best fit" is placed among these points plotted on a coordinate system, would the slope of this line be positive or negative?
4)Answer the following:
- If the correlation coefficient is -0.53, what is the sign of the slope of the regression line?
- As the correlation coefficient increases from 0.51 to 0.56, do the points of the scatter plot move toward the regression line, or away from it? (Point3)
6. Determine whether each of the distributions given below represents a probability distribution. Justify your answer.
(A)

x	1	2	3	4
P(x)	1/3	7/12	1/4	0

(B)

x	3	6	8
P(x)	0.4	1/4	0.3

(C)

x	20	35	40	50
P(x)	0.5	-0.2	0.3	0.4

7. Two marbles are selected, one at a time from a jar of marbles containing 10 black, 10 brown, 10 white and 10 green marbles. Let x represent the number of white marbles selected in 2 separate selections from the jar.
(A) If this experiment is completed without replacing the marbles each time, explain why x is not a binomial random variable.
(B) If this experiment is completed with replacement of the marbles each time, explain why x is a binomial random variable.
(Points : 4)
8. You are given the following data.

Number of Absences	Final Grade
0	93
1	92
2	84
3	77
4	67
5	59

- Find the correlation coefficient for the data.
- Find the equation for the regression line for the data, and predict the final grade of a student who misses 3.5 days. (Points : 6)

005_4bvp5k-lvpqroqt.docx

Robert · Accepted Answer

Sol: 1 
          ( )A  They have a positive linear correlation. 
           ( )B 70(from the graph we can see that the pre test score 70 is equal to 70 
post test score). 
            ( )C  The slope of the “line of best fit” is positive. 
Sol: 2 
               n 15,x 4,p 0.5    
                Probability     
4 1115
4 0.5 0.5C  
                        Probability 0.04165
Sol: 3 
    A  Would the correlation between  and x y  in the table above be positive or 
negative? 
         The correlation between  and x y  in the table is Negative because as x
increases y decreases. 
 B  Find the missing value of y  in the table. 
     0y  , (because we see that as x increases by 1, y increases by 1) 
 C  How would the values of this table be interpreted in terms of linear regression?  
    The values in the table when plotted will give straight line graph. The fit will 
be perfectly linear. 
 D  If a "line of best fit" is placed among these points plotted on a coordinate 
system, would the slope of this line be positive or negative?  
    When these points plotted on a coordinate system, then the slope of this line 
would be negative.
Sol: 4 
 A  If the correlation coefficient is -0.53, what is the sign of the slope of the 
regression line? 
      Positive (Since correlation coefficient is -0.53 which is negative. So the sign of 
the slope is same as that of the correlation coefficients). 
 B  As the correlation coefficient increases from 0.51 to 0.56, do the points of the 
scatter plot move toward the regression line, or away from it?  
      Towards the line (Since there is much stronger association between  and yx
now).
Sol: 6    Here, we use the fact that for a probability distribution to be valid, the sum 
of  P x should be 1.

1. The scatter plot below shows the relationship between pre-test and post-test scores in a Statistics class. The horizontal axis represents the pre-test scores. Use this graph to answer the questions...

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