1) 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?
For the table that follows, answer the following questions:
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?
2) 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?
3) 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)
(C)
|
x
|
20
|
35
|
40
|
50
|
|
P(x)
|
0.5
|
-0.2
|
0.3
|
0.4
|
4) 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.
5) 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.