Download Math 165.X1.sobieraj.3.7.07 KEY Show all work to receive full credit

Math 165.X1.sobieraj.3.7.07
KEY
Show all work to receive full credit……
Part 1: (10 points) Answer True or False to the following.
T
1. A categorical variable can name categories with either names or numerals.
F
2. A 5-number summary is used to describe categorical variables.
T
3. A distribution is skewed to the left, if it contains a large number of high values.
F
4. A stem-and-leaf plot shows the same information as a histogram.
F
5. You have just bought a new car with a claim that highway fuel efficiency is
31 miles per gallon. You expect that cars like yours will have an IQR of 35 miles per
gallon.
Part 2: Show all work to receive full credit……
1. In 2000, a high school class was surveyed prior to graduation about their plans. The
table below summarizes the results for white and minority students.
4-year
college
2-year
college
Military
Employment
Other
totals
White
198
Minority
44
totals
242
36
6
42
4
14
16
268
1
3
3
57
5
17
19
325
82.5%
a. What percent of graduates are white? 268/325
12.9%
b. What percent of graduates are planning to attend a 2-year college?
42/325
13.4%
c.
What percent of the white graduates are planning to attend a 2-year
college? 36/268
85.7%
d.
What percent of the graduates planning to attend a 2-year college are
white? 36/42
2. The National Center for Education Statistics reported 1999 average math scores for 8th
graders in 38 nations. (Singapore got the highest score and the US scored 502.)
The summary statistics for the average scores for the 38 nations is below.
Summary of Math
Scores
Count
Mean
Median
StdDev
Min
Max
Q1
Q3
a.
38
487.211
499
72.3203
275
604
448
531
Draw a boxplot of the above data.
700
600
500
400
300
200
Math Scores
b. Explain why there is a difference between the mean and the median. The mean is
lower than the median of a number of low scores.
c. Comment on the performance of the United States. The US scored a little better
than half of the countries and was 15 points above the mean score.
(30 points) 3. A forester measured 27 of the trees in a large woods that is up for sale.
He found a mean diameter of 10.4 inches and a standard deviation of 4.7 inches.
Suppose that these trees provide an accurate description of the whole forest and that a
Normal model applies. Include a sketch with your calculations.
a. What diameter would you expect at least 25% of the trees to have?
y "10.4
".67 =
#
#$ y = 7.25"
4.7
b. What size would you expect the central 95% of all trees to be?
!
±1.96 =
y "10.4
#
#$ y = 1.188, 19.612
4.7
c. About what percent of the trees should be less than an inch in diameter?
!
z=
Using the z-table: 2.28%
1"10.4
= "2
4.7
d. About what percent of the trees should be between 5.7 and 10.4 inches in
!
diameter?
5.7 "10.4
z=
= "1
4.7
Using the z-table: 50% - 15.87% = 34.13%
!
e. About what percent of the trees should be over 15 inches in diameter?
z=
15 "10.4
= .979
4.7
Using the z-table: 100% - 83.65% = 16.35%
!
(15 points) 4. A survey was conducted in the US and 10 countries of Western
Europe to determine the percentage of teenagers who had used marijuana and other
drugs. The results are summarized in the table below.
Country
Percent Who Have Used
Marijuana Other Drugs
CzechRep
Denmark
England
Finland
Ireland
Italy
No.Ireland
Norway
Portugal
Scotland
USA
22
17
40
5
37
19
23
6
7
53
24
4
3
21
1
16
8
14
3
3
31
24
a. Create a scatterplot of the data on your calculator and describe what you see.
The points are arranged somewhat linearly, in a positive direction.
b. What is the correlation between the percent of teens who have used marijuana and
the percent who have used other drugs? 0.934
c. Should marijuana be considered a “gateway” drug that leads to use of other drugs?
Explain your answer.
Although there is a strong association between use of marijuana and other drugs,
it can’t be said that use of marijuana leads to use of other drugs. There could be
other variables that are involved in the use of other drugs.