Download Ethan Frome - Hope College Math Department

Math 210
Test 1
February 5, 2004
Name__________________________________
Questions 1-10 are multiple choice. Circle the letter of the best response on answer sheet.
[3 pts each]
1) The frequency histogram to the right displays a set of
measurements. What is true about the median, m, of
this data set?
a) 0 < m < 1
b) m = 0.5
c) m = 1
d) m > 1
e) None of the above.
2) Using the histogram from question 1, which of the following is true?
a)
b)
c)
d)
The mean is larger than the median.
The mean is smaller than the median.
The mean and median are approximately equal.
It is impossible to compare the mean and median for these data.
3) A professor teaches two statistics classes. The first class has 20 students and their mean on the
first test was 84. The second class has 30 students and their mean on the same test was 74.
What is the mean on this test if the professor combines the scores for both classes?
a) 76
b) 78
c) 79
d) 80
e) The mean cannot be calculated since individual scores of each student are not available.
4) The following table (from Minitab) gives descriptive statistics for the weights (in ounces) of
200 newborns from in North Carolina. If a baby has a weight such that his or her standardized
weight is z = 1.4, what is his or her weight?
Descriptive Statistics: Weight
Variable
Weight
a)
b)
c)
d)
e)
N
200
Mean
114.70
31.71 ounces
82.99 ounces
146.41 ounces
148.21 ounces
None of the above
Median
116.50
StDev
22.65
Minimum
14.00
Maximum
170.00
Q1
105.00
Q3
128.00
5) In the scatterplot below, a least-squares regression line has been fitted to the heights of Robert
Wadlow for ages 5 through 22 (as done in lab). His height at birth (age 0) was then plotted (as
the double circle on the left side of the graph). Which of the following statements correctly
describes how adding his birth height would change the correlation and the regression equation
from what it is shown in the graph to what it would be for ages 0 through 22?
110
100
Height (inches)
90
80
70
60
50
40
30
20
0
10
20
Age (years)
a) The age 0 point will make the regression line steeper and the correlation stronger.
b) The age 0 point will make the regression line steeper and the correlation weaker.
c) The age 0 point will make the regression line closer to horizontal and the correlation
stronger.
d) The age 0 point will make the regression line closer to horizontal and the correlation
weaker.
e) The age 0 point will not have any effect on the regression line since it follows the same
downward trend.
6) A large elementary school has 15 classrooms, with 24 children in each classroom. A sample of
30 children is chosen by the following procedure. Each of the 15 teachers selects 2 children
from his or her classroom to be in the sample by numbering the children from 1 to 24, then
using a random digit table to select two different random numbers between 01 and 24. The 2
children with those numbers are in the sample. Did this procedure give a simple random
sample of 30 children from the elementary school?
a)
b)
c)
d)
e)
No, because the teachers were not selected randomly.
No, because not all possible groups of 30 children had the same chance of being chosen.
No, because not all children had the same chance of being chosen.
Yes, because each child had the same chance of being chosen.
Yes, because the numbers were assigned randomly to the children.
7) A study is conducted to determine if one can predict the number of traffic accidents based on
the amount of snowfall. The response variable in this study is
a)
b)
c)
d)
e)
the amount of snowfall.
the number of traffic accidents.
the experimenter.
the age of the driver or any other variable that may explain the an accident.
none of the above.
8) X and Y are two categorical variables. The best way to determine if there is a relationship
between these two variables is to
a)
b)
c)
d)
e)
calculate the correlation between X and Y.
draw a scatterplot of the X and Y values.
draw side-by-side boxplots of the X and Y values.
make a two-way table of the X and Y values.
All of the above.
9) Correlation measures
a)
b)
c)
d)
e)
whether there is a relationship between two variables.
whether or not a scatterplot shows an interesting pattern.
whether a cause and effect relationship exists between two variables.
the strength of a straight-line relationship between two variables.
None of the above.
10) A study of human development showed two types of movies to groups of children. Crackers
were available in a bowl, and the investigators compared the number of crackers eaten by
children watching the different kinds of movies. One kind was shown at 8 A.M. and another at
11 A.M. It was found that during the movie shown at 11 A.M., more crackers were eaten than
during the movie shown at 8 A.M. The investigators concluded that the different types of
movies had an effect on appetite. A lurking variable in this experiment is
a)
b)
c)
d)
e)
the number of crackers eaten.
the different kinds of movies.
the time the movie was shown.
the bowls.
the investigators.
11) Some statistics students measured the time it took drivers to go through the drive-thru at a local
Wendy’s restaurant. Twenty of these times, in seconds, are as follows. Use the area below for
parts (a) and (f). [16 pts]
50, 175, 65, 68, 87, 114, 116, 125, 127, 150, 50, 52, 45, 85, 102, 108, 58, 63, 84, 80
a) Make a stem and leaf diagram of the data use the tens
place for the stem and the units place for the leaf
b) Find the median time.
c) Find the first and third quartiles.
d) Find the mean, x , of the sample.
e) Find the standard deviation, s, of the sample.
f) Make a box and whisker diagram (boxplot) for the data
and include a scale.
b) ___________________
c) ___________________
d) ___________________
e) ___________________
12) The following graph shows a scatter plot with regression line of wine consumption (liters of
alcohol from wine per person per year) and yearly deaths from heart disease (deaths per
100,000 people) in 19 developed nations. [14 pts]
(per 100,000 people)
Deaths From Heart Disease
300
200
100
0
1
2
3
4
5
6
7
8
9
Wine Consumption
(liters of alcohol from wine per person per year)
a) What is the explanatory variable?
b) What is the response variable?
c) Using the regression equation, yˆ  260.6  23.0 x , what is the predicted deaths per 100,000
people in a country that consumes 5 liters of alcohol per person per year?
d) Briefly explain what the slope and y-intercept mean in the regression equation in terms of
deaths and wine consumption. Use the numbers given in the regression equation in your
explanation.
13) Does how long young children remain at the lunch table help predict how much they eat? Here
are data on 13 toddlers observed over several months at a nursery school. “Time” is the
average number of minutes a child spent at the table when lunch was served. “Calories” is the
average number of calories the child consumed during lunch. [12 pts]
Time
21.4
Calories 472
30.8
498
37.7
465
33.5
456
32.8
423
39.5
437
22.8
508
34.1
431
33.9
479
43.8
454
42.4
450
43.1
410
29.2
504
a) Find a regression equation for predicting average calories consumed given average time
spent at the lunch table.
b) Find the correlation between average time at the lunch table and average number of calories
consumed.
c) Based on either your regression equation or correlation, for children that sit at the lunch
table for longer than average periods of time will they consume more or fewer calories than
average?
d) Find the residual for the first child in the sample with a time of 21.4 minutes and calories
consumed of 472.
14) In 2003 the composite scores for the ACT test were normally distributed with a mean of
 = 20.8 points and a standard deviation of  = 4.8 points. For each question include both the
answer along with a sketch of an appropriately shaded normal curve with mean and other
important points mark. Also, if you are doing these with the distributions menu on a TI-83
write down the input from your calculator. [15 pts.]
a) What percent of all those taking the test had scores of 18 or less?
b) What percent of the scores were between 18 and 28?
c) To be in the highest 2% of scores, above what score would someone have to be?
15) The following two-way table categorizes the class standing at Hope College for men and
women for Fall 2003. Leave your answers as fractions. [13 pts]
CLASS
Freshmen
Sophomore
Junior
Senior
Non-Degree
Total
Male Female Total
309
526
835
263
456
719
271
426
697
286
459
745
33
39
72
1162
1906
3068
a) What proportion of all Hope students are juniors?
b) What proportion of the sophomores are males?
c) What proportion of the males are juniors?
d) Suppose you are planning to randomly choose one student from the freshman class and
one student from the junior class. Which is more likely to be male, the freshmen or the
junior? Explain your answer using the appropriate proportions or percents.