Statistics: Diet and Weight

Extracted Content from Question Files:

The scatter plot below shows the relationship between the number of
1.
weeks and adult spent dieting and the adult’s weight in pounds. The
horizontal axis represents the number of weeks of dieting. Use this
graph to answer the questions below.

(A) How would you describe the relationship between the number of weeks
on the diet and the adult’s weight?
(B) Approximately what did the dieter weigh in the 5th week of dieting?
(C) Would the slope of the "line of best fit" be positive or negative?

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 -1
2 1
3 3
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?
(Points : 4)

4. Answer the following:
- If the correlation coefficient is 0.41, what is the sign of the slope of
the regression line?
- As the correlation coefficient increases from 0.85 to 0.88, do the points
of the scatter plot move toward the regression line, or away from it? (Points :
4)

5. For each of the scatterplots below, determine whether the correlation
coefficients represented would be positive, negative, or near zero.

6. Determine whether each of the distributions given below represents a
probability distribution. Justify your answer.

(A)
x 1 2 3 4
P(x) 1/4 1/12 1/3 1/6

(B)

x 3 6 8
P(x) 0.2 2/5 0.3

(C)

x 20 30 40 50
P(x) 3/10 - 0.5 0.3
0.1

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.

8. You are given the following data.

Number Final
of Grade
Absences
0 93
1 93
2 77
3 68
4 65
5 54

- 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)