Download Math 210 - Hope College Math Department

Math 210
Final Exam
Spring 2001
Name _____________________________________
Questions 1 - 4 are multiple choice. Circle the letter of the best response. [4 pts each]
a) The mean is smaller than the median.
b) The mean is larger than the median.
c) The mean and the median have the same value.
d) There is no way to tell which is larger without
the actual data.
20
Frequency
1) The following histogram is the distribution of dates
(since 1900) of pennies. Using this graph to
estimate the mean and median dates of pennies, we
can conclude:
10
0
60
70
80
90
100
pennies
2) 95% confidence interval for the mean, , of a population is computed from a random
sample and found to be 9 ± 3. We may conclude:
a) 95% of the data are between 6 and 12.
b) There is a 95% probability that the true mean is 9 and a 95% chance the true
margin of error is 3.
c) If we took many, many additional random samples and from each computed a
95% confidence interval for , approximately 95% of these intervals would
contain .
d) There is a 95% chance that x is between 6 and 12.
3) The P-value of a test of a null hypothesis is:
a) The probability, assuming the null hypothesis is true, that the test statistic will
take a value at least as extreme as that actually observed.
b) The probability, assuming the null hypothesis is false, that the test statistic will
take a value at least as extreme as that actually observed.
c) The probability the null hypothesis is true.
d) The probability the null hypothesis is false.
4) When performing an ANOVA, the F-statistic that is acquired is made up of the ratio
of two numbers. Which statement best describes those two numbers?
a) The numerator is a measure of the variability within the different groups and the
denominator is a measure of how large the means are.
b) The numerator is a measure of how large the means are and the denominator is a
measure of the variability between the groups.
c) The denominator is a measure of the variability between the different groups and
the numerator is a measure of the variability within the groups.
d) The numerator is a measure of the variability between the different groups and the
denominator is a measure of the variability within the groups.
5) The following two-way table categorizes enrollment at Hope College for this junior.
Assume a student is chosen at random.
Let J = a student chosen is a junior and let W = the student chosen is a woman. Find
the following probabilities. (Leave answers in fraction form.) [10 pts.]
CLASS
Freshman
Sophomore
Junior
Senior
Special
Total
MEN
297
315
244
290
63
1209
WOMEN
481
429
408
429
59
1806
Total
778
744
652
719
122
3015
a) P( J and W)
b) The probability that someone is not a junior.
c) The probability that a man is chosen given that you are just choosing out of the
sophomore class.
d) P(W | J)
e) P(J or W)
6) According to a Harris Poll 70% of Americans like meat loaf. Suppose that 3
Americans were chosen at random. Complete the following probability distribution
where X is the number of Americans that like meat loaf and P(X) is the probability of
obtaining exactly X Americans that like meat loaf in your sample. [8 pts.]
X
P(X)
0
1
2
3
7) According to a Gallup Poll 40% of Americans have attended church or synagogue in
the last week. If a random sample of 10 Americans is taken, what is the probability
that at least 1 of them will has attend church or synagogue in the last week? [6 pts.]
8) The lengths of newborn children in the United States vary according to the normal
distribution with mean 19.5 inches and standard deviation 0.75 inches. [12 pts.]
a) What is the probability that a baby chosen at random is more than 20 inches in
length?
b) You choose 5 babies at random. What is the probability that their average birth
length is more than 20 inches?
c) To be in the highest 5% of lengths, above what length would a baby have to be?
9) I weighed 17 small Payday candy bars for class. The sample mean was,
x  21.87 grams, and the sample standard deviation was, s = 0.97 grams. Find a 95%
confidence interval for the population mean weight for this type of candy bar. [8 pts]
10) Scores this year on the SAT Mathematics test (SAT-M) for students taking the test for
the first time are believed to be normally distributed with mean 1. For students
taking the test for the second time, this year's scores are also believed to be normally
distributed but with a possibly different mean 2. A random sample of the SAT-M
scores of 100 students who took the test for the first time this year was obtained and
the mean of these 100 scores was x1  504.5 , and the standard deviation was s1 =
100. A random sample of the SAT-M scores of 30 students who took the test for the
second time this year was also obtained and the mean of these 30 scores was
x2  539.1 and the standard deviation was s2 = 90. Test the hypothesis that those
taking the SAT-M for the second time have higher scores than those taking it for the
first time. (Let  = 0.05.) Make sure you include the hypotheses, test statistic, Pvalue, and conclusion. [10 pts]
11) This semester, 10 out of 26 students in our course indicated that they liked Pepsi over
Coke. Consider our class as a random sample of all Hope College students and find a
95% confidence interval for the proportion of all Hope students that prefer Pepsi over
Coke. [8 pts]
12) In a Gallup poll conducted on April 20-22 this year, 62% of the 1015 polled approved
of the way GW Bush is performing his job. At the beginning of the Clinton
presidency eight years ago, 55% of 1008 polled approved of the way Clinton was
performing his job. Do these proportion show that a greater proportion of Americans
approve of Bush's performance now than those that approved of Clinton's
performance eight years earlier? Test this hypothesis with  = 0.05. Make sure you
include the hypotheses, test statistic, P-value, and conclusion. [10 pts]
13) Three types (beef, poultry, and meat) of hot dog were tested for sodium level. The
data from an ANOVA test run on Minitab is given below
Analysis of Variance for Sodium
Source
DF
SS
MS
Type
2
31739
15869
Error
51
455249
8926
Total
53
486988
F
1.78
P
0.179
Complete the ANOVA test by stating the hypotheses, giving the test statistic, giving
the P-value, and stating a conclusion. [8 pts]