Download Practice Test 2 Math 4753 — Summer 2005 This test is worth 100

Practice Test 2
Math 4753 — Summer 2005
This test is worth 100 points. Questions 1 – 5 are worth 4 points each. Circle the letter of
the correct answer. Each question in Question 6 – 9 is worth the same number of points but
different parts within the questions are not necessarily worth equal amounts of points. Any
work for partial credit must be shown on this sheet. Mark answers in the spaces provided.
No credit will be given if work is not shown. There is no partial credit for the multiple
choice questions.
1. A confidence interval for a proportion indicates that the proportion is likely greater than
one half if:
a. .5 is in the confidence interval.
b. .5 is below the lower confidence limit.
c. .5 is above the upper confidence limit.
d. a, b, and c are all true.
e. Exactly two of a, b, and c are true.
2. A confidence interval for a mean is wider than another confidence interval for the same
mean if:
a. The n is larger for the first confidence interval.
b. The α for the first confidence interval is larger.
c. The y for the first confidence interval is larger than that for the second
confidence interval but both have the same standard deviation s (and the same α and
n).
d. a, b, and c are all true.
e. Exactly two of a, b, and c are true.
3. A confidence interval for the ratio of two variances shows that one of the variances is
greater than the other if.
a. 1 is in the confidence interval.
b. Both limits of the confidence interval are less than 1.
c. Both limits of the confidence interval are greater than 1.
d. a, b, and c are all true.
e. Exactly two of a, b, and c are true.
4. For a χ 2 -distribution, we know:
a. The distribution is symmetrical.
b. χα2 = − χ1−2 α for the same degrees of freedom.
2
2
c. The area under the χ 2 pdf above χ1−2 α is the same as the area under the χ 2 pdf
2
below χ
2
α
2
for the same degree of freedom.
d. a, b, and c are all true.
e. Exactly two of a, b, and c are true.
5. If the test statistic of a hypothesis test does not fall in the rejection region for that
hypothesis test then:
a. We likely have made a mistake in calculating the value of the test statistic.
b. We accept H 0 .
c. We must continue to use H 0 as a working hypothesis.
d. a, b, and c are all true.
e. Exactly two of a, b, and c are true.
6. Suppose that a random sample of 8 OU mechanical engineering majors had an average
GPA of 3.54 with a standard deviation of .25 while a random sample of 9 Texas A&M
mechanical engineering majors had an average GPA of 3.02 with a standard deviation of
.40.
a. Find a 98% confidence interval that will allow you to decide whether the variances
are the same and, if not, which is greater.
b. Based on the confidence interval in a, can we assume that the variance of the GPAs
of mechanical engineering students at Texas A&M is greater than that of similar
students at OU? Tell how you know.
7. A production line produces rulers that are supposed to be 12 inches long. A sample of 49
of the rulers had a mean of 12.1 and a standard deviation of .5 inches.
a. Find a 95 percent confidence interval to estimate the actual mean length of the
population of rulers made on the production line.
b. Given this confidence interval, is it likely that the population mean is 12 inches as it
is supposed to be? Tell how you know.
8. A sample of 20 OU freshmen had a mean GPA of 2.8 over all their courses taken in their
first semester at OU. This had a variance of .25. Perform a hypothesis test at the 95
percent level to determine if the first semester GPA of all OU freshmen is less than a B
(3.0).
a. What is the null hypothesis?
b. What is the alternative hypothesis?
c. What is the value of the test statistic?
d. What is the rejection region (with its numerical value)?
e. What conclusion do you draw?
f. What does this mean in terms of the problem situation?
9. A survey of 200 regular viewers of Channel 5 in Oklahoma City show that 68 believe that
Gary England is God. A survey of 100 regular viewers of Channel 9 in Oklahoma City show
that 68 of them also believe that Gary England is God. Given these data perform a 90
percent hypothesis to determine if the proportion of Channel 9 viewers who believe that
Gary England is God is greater than the proportion of Channel 5 viewers who believe it.
a. What is the null hypothesis?
b. What is the alternative hypothesis?
c. What is the value of the test statistic?
d. What is the rejection region (with its numerical value)?
e. What conclusion do you draw?
f. What does this mean in terms of the problem situation?