aIntro
to Stats, Test 1
R.
Sinn, Spring 2007 Name
______________________________
Test is out of 90 Points Total
Directions
Answer each question in full.
In some cases in statistics, more than one answer may be counted correct. Please justify your statements if in doubt.
You may use a graphing calculator on any problem.
Please mark “CALC” in the
margin next to any steps performed on
the calculator.
Questions 1 and 2 relate to Histogram
1 shown at right.
1.
[5 Points] Check all the statements that apply:
q The distribution is
approximately normal.
q The distribution is skewed
left.
q The distribution is skewed
right.
q The mean and median are approximately
equal.
2.
[5 Points] Check all the statements that apply:
q The mean is likely to be less
than the median.
q The mean is likely to be greater
than the median.
q The data set is not
likely to contain outliers.
q Outliers likely exist, and
the majority are on the left.
q Outliers likely exist, and
the majority are on the right.
Questions 3 and 4 relate to Histogram
2 shown at right.
3.
[5 Points] Check all the statements that apply:
q The distribution is
approximately normal.
q The distribution is skewed
left.
q The distribution is skewed
right.
q The mean and median are approximately
equal.
4.
[5 Points] Check all the statements that apply:
q The mean is likely to be
less than the median.
q The mean is likely to be
greater than the median.
q The data set is not
likely to contain outliers.
q Outliers likely exist, and the
majority are on the left.
q Outliers likely exist, and the
majority are on the right.
|
Regression Statistics |
Line of Best Fit y = a x + b |
||
|
r |
-0.4827 |
a |
-0.372 |
|
R2 |
0.2230 |
b |
7.483 |
5.
[10 Points] Essay: During the Fall semester 2006, a team of NGCSU
students found a correlation between age (x-variable,
measured in years) and interest in rock climbing (y-variable, measured on a scale from 1 – 10, with 10 indicating high
interest and 1 indicating no interest).
Write 2 – 5 complete sentences explaining everything you know
and can infer based upon the output shown to the right. Be sure to focus your analysis upon
real-world implications.
6.
[5 Points] A statistician computes a regression comparing a father’s
height (in inches) to his daughter’s height (in inches). She finds that R2 = .39. Interpret this finding.
7.
[5 Points] Given Scatter Plot 1 shown at right, check all the
statements that apply:
q Linear Regression is
appropriate.
q Linear Regression is not
appropriate.
q The (linear) correlation is positive.
q The (linear) correlation is negative.
q The (linear) correlation is strong.
q The (linear) correlation is weak.
q No linear correlation
exists.
8.
[5 Points] Given Scatter Plot 2 shown at right, check all the
statements that apply:
q Linear Regression is
appropriate.
q Linear Regression is not
appropriate.
q The (linear) correlation is positive.
q The (linear) correlation is negative.
q The (linear) correlation is strong.
q The (linear) correlation is weak.
q No linear correlation
exists.
9.
[10 Points] A tallish female college student was studying dating
patterns. She wonders if tall women tend
to date taller men than do short women. She measures the height of several
women in her dorm; then she measures the next man each woman dates. Here are
the data (heights in inches), and linear regression is appropriate:
|
Women (x) |
66 |
64 |
66 |
65 |
70 |
65 |
|
Men (y) |
72 |
68 |
70 |
68 |
71 |
65 |
a.
Find the correlation coefficient and analyze it.
b. If a woman is 5’5” tall,
estimate the height of her boyfriend.
c.
Analyze R2 in the context of this problem.
d. Analyze the slope of the
prediction equation. How meaningful is
this relationship (the one between the variables, not the dating
relationships)? Hint: refer to your
answer in part (c).
|
Record year x-variable |
Time
(seconds) y-variable |
|
1967 |
2286.4 |
|
1970 |
2130.5 |
|
1975 |
2100.4 |
|
1975 |
2041.4 |
|
1977 |
1995.1 |
|
1979 |
1972.5 |
|
1981 |
1950.8 |
|
1981 |
1937.2 |
|
1982 |
1895.3 |
|
1983 |
1895.0 |
|
1983 |
1887.6 |
|
1984 |
1873.8 |
|
1985 |
1859.4 |
|
1986 |
1813.7 |
|
1993 |
1771.8 |
10. [10 Points] The table to the
right shows the progress of women’s world record times (in seconds) for the
10,000-meter run. Answer the following:
a.
Find and analyze the correlation between record time and year.
b. Analyze R2 in the
context of this problem.
c.
In what year (according to your prediction equation) will the women’s
10,000-meter world record time be 5 minutes?
d. Explain why the correct
answer to part (c) makes very little sense in a real-world context.
11.
[5 Points] Five
hundred drivers were asked about the age car they drive (in years). The boxplot below shows the data collected on
the ages of the 500 cars. For parts (a)
through (c), select the one best answer choice.
), standard deviation (s)
and sample size (n).