Practice Exam 2015-2016

Statistical Methods in Economics (ECON1003)

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

1) For the following scatter plot, what would be your best estimate of the correlation 1)
coefficient?

A) 1.0 B) 0.3 C) 0.1 D) 0.7

2) Consider the following probability distribution. Which of the following is true? 2)

x 0 1 2 3 4 5 6
P(x) 0.07 0.19 0.23 0.17 0.16 0.14 0.04

A) P(2 ≤ X ≤ 5) = 0.33 B) P(X > 3) = 0.51

C) P(X ≥3 ) = 0.51 D) P(X < 6) =1

3) What proportion of the total area under the normal curve is within ± two standard deviations 3)
of the mean?
A) About 68% B) About 95% C) About 99.7% D) About 50%

4) If the random variable X is exponentially distributed with parameter λ = 4, then the 4)

probability P(X ≤ 0.25) is equal to:
A) 0.5000 B) 0.3679 C) 0.2500 D) 0.6321

5) Which of the following is not a characteristic for a normal distribution? 5)

A) The mean, median, and mode are all equal.
B) It is a bell-shaped distribution.
C) It is symmetrical distribution.
D) The mean is always zero.

6) All possible random samples of 200 middle managers are selected from a population for a 6)
study concerning their mean annual income. The population standard deviation is computed
to be $2,248.5. What is the standard deviation of the sampling distribution of the means?
A) $57.86 B) $158.99 C) $11.24 D) $47.42

7) Random samples of size 36 each are taken from a large population whose mean is 120 and 7)
standard deviation is 39. The standard error of the sampling distribution of sample mean is:
A) 6.5 B) 15.6 C) 24.5 D) 39

1
 8) A golfer practices 60 twenty-foot putts a day and historically makes 25 percent of them. 8)
Calculate the standard error of the sample proportion.
A) 0.4057 B) 0.6258 C) 0.3256 D) 0.0559

9) If all possible samples of size n are drawn from an infinite population with a mean of 20 and 9)
a standard deviation of 5, then the standard error of the sampling distribution of sample
means is equal to 1.0 only for samples of size:
A) 5 B) 25 C) 15 D) 20

10) Interval estimates for the variance of a normal population rely on the random variable (n - 10)
1)s 2 / σ2, which follows:
A) a normal distribution. B) a binomial distribution.
C) a chi-square distribution. D) the Poisson distribution.

11) A random sample of size 15 is taken from a normally distributed population with a sample 11)
mean of 75 and a sample variance of 25. The upper limit of a 95% confidence interval for the
population mean is equal to:
A) 74.727 B) 79.273 C) 72.231 D) 77.530

12) Let X1, X2, X3 , and X4 be a random sample of observations from a population with mean ! 12)
^ = 0.15 X + 0.35 X + 0.20 X + 0.30
and variance σ 2. Consider the following estimator of !: θ 1 1 2 3
^?
X4. What is the variance of θ 1
A) 0.275 σ 2 B) 0.20 σ2 C) 0.55 σ2 D) 0.125 σ2

13) Which of the following distributions is used when estimating the population mean from a 13)
normal population with unknown variance?
A) the t distribution with n - 1 degrees of freedom
B) the t distribution with n + 1 degrees of freedom
C) the t distribution with 2n degrees of freedom
D) the t distribution with n degrees of freedom

14) Suppose you have the following null and alternative hypotheses: H0 : ! = 8.3 and H1 : ! ≠ 8.3. 14)
You take a sample of 30 observations, and find a sample mean of 7.3 with a standard
deviation of 3.2. Which of the following is the most accurate statement about the p-value?
A) p -value < 0.01 B) p-value > 0.10
C) 0.01 < p -value < 0.05 D) 0.05 < p-value < 0.10

15) If testing for the difference between the means of two related populations, with samples of 15)
sizes n 1 = n 2 = n, where the variance of the differences is unknown, what is the number of
degrees of freedom?
A) 2(n - 1) B) n - 2 C) 2n - 1 D) n - 1

16) A regression analysis between sales (in $1000) and advertising (in $) resulted in the following 16)
least squares line: ^
y = 80,000 + 4x. This implies that:
A) an increase of $4 in advertising is expected to result in an increase of $4,000 in sales.
B) an increase of $1 in advertising is expected to result in an increase of $4,000 in sales.
C) an increase of $1 in advertising is expected to result in an increase of $4 in sales.
D) an increase of $1 in advertising is expected to result in an increase of $80,000 in sales.

2
THE NEXT QUESTION IS BASED ON THE FOLLOWING INFORMATION:
In a furniture manufacturing plant, a customer survey indicates that blemishes in the finish are a major concern. The
table shown below displays a quality manager's probability assessment of the number of defects in the finish of new
furniture.

Number of Defects 0 1 2 3 4 5
Probability 0.34 0.25 0.19 0.11 0.07 0.04

17) Let event A be that there are more than three defects and let event B be that there are four or 17)
fewer defects. Which of the following statements is true?
A) P(A ∪ B) = 0.07
B) Events A and B are mutually exclusive.
C) Events A and B are collectively exhaustive.
D) P(A ∩ B) = 0.18

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING:

The probability that a person catches a cold during the cold and flu season is 0.4. Assume that 10 people are chosen at
random.
18) What is the standard deviation for the number of people catching a cold? 18)
A) 1.265 B) 1.125 C) 1.245 D) 1.549

19) What is the probability that exactly four of them will catch a cold? 19)
A) 0.2508 B) 0.7502 C) 0.3670 D) 0.6330

THE NEXT QUESTION IS BASED ON THE FOLLOWING INFORMATION:

The number of beverage cans produced each hour from a vending machine is normally distributed with a standard
deviation of 8.6. For a random sample of 12 hours, the average number of beverage cans produced was 326.0. Assume
a 99% confidence interval for the population mean number of beverage cans produced per hour.

20) Find the upper confidence limit of the 99% confidence interval. 20)
A) 325.98 B) 340.25 C) 319.59 D) 332.41

THE NEXT QUESTION IS BASED ON THE FOLLOWING INFORMATION:

Independent random sampling from two normally distributed populations gives the following results:
n x = 55, x = 520, σ x = 30, n y = 45, y = 482, and σy = 24

21) Find the margin of error for a 98% confidence interval for the difference in the means of the 21)
two populations.
A) 12.58 B) 19.86 C) 8.50 D) 15.77

THE NEXT QUESTION IS BASED ON THE FOLLOWING INFORMATION:

In a random sample of 150 large retailers, 110 used regression as a method of forecasting. In an independent random
sample of 180 small retailers, 90 used regression as a method of forecasting.

22) Find the margin of error for a 90% confidence interval. 22)
A) 0.1453 B) 0.0854 C) 0.0482 D) 0.1792

3
THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
The residents of Austin, Texas, complain that parking fines given in their city are higher than the parking fines that are
given in Houston. Independent random samples of the amounts paid by residents for parking tickets in each of two
cities over the last four months were obtained. Assume the population variances are equal. These amounts were as
follows:

Austin 80 125 144 98 138 100 129 113 132 115

Houston 98 85 114 100 76 85 120 105

23) Find the 98% confidence interval for the difference in the mean costs of parking tickets in 23)
these two cities.
A) 19.52 ± 22.21 B) 19.52 ± 25.37 C) 19.52 ± 20.38 D) 19.52 ± 22.77

24) What is the sample variance of the parking fines issued in Austin? 24)
A) 201.86 B) 404.49 C) 230.69 D) 364.04

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:

Consider the data in the table below.

Group 1 150 140 122 85 126 105 130 118 121 100
Group 2 120 95 132 65 101 78 111 99

25) Find the 95% confidence interval for the difference in the mean costs of parking tickets in 25)
these two cities.
A) 19.57 ± 18.98 B) 19.57 ± 20.00 C) 19.57 ± 17.68 D) 19.57 ± 20.38

26) Calculate the pooled sample variance. 26)

A) 699.121 B) 410.936 C) 590.876 D) 680.789

THE NEXT QUESTION IS BASED ON THE FOLLOWING INFORMATION:

A large milling machine produces steel rods to certain specifications. The machine is considered to be running
normally if the standard deviation of the diameter of the rods is at most 0.15 millimeters. The line supervisor needs to
test the machine is for normal functionality. The quality inspector takes a sample of 25 rods and finds that the sample
standard deviation is 0.19.

27) Which of the following statements is the most accurate? 27)

A) Fail to reject null hypothesis at α ≤ 0.10
B) Reject null hypothesis at α = 0.01
C) Reject null hypothesis at α = 0.025
D) Reject null hypothesis at α = 0.05

THE NEXT QUESTION IS BASED ON THE FOLLOWING INFORMATION:

Two samples each of size 20 are taken from independent populations assumed to be normally distributed with equal
variances. The first sample has a mean of 43.5 and standard deviation of 4.1 while the second sample has a mean of
40.1 and standard deviation of 3.2. A researcher would like to test if there is a difference between the population
means at the 0.05 significance level.

28) Based on the given information, the p-value for the F test of equal variances can be calculated 28)
and shown to be 0.289. Based on this p-value, what is your conclusion?
A) The assumption of equal variances is correct.
B) The variance of the first sample is greater than the other.
C) The answer cannot be determined based on this p -value.
D) The assumption of equal variances is incorrect.

4
THE NEXT QUESTION IS BASED ON THE FOLLOWING INFORMATION:
Suppose two food preservatives are extensively tested and determined safe for use in meats. A processor wants to
compare the preservatives for their effects on retarding spoilage. Suppose 16 cuts of fresh meat are treated with
preservative A and another 12 cuts of meat are treated with preservative B. The number of hours until spoilage begins
is recorded for each of the 28 cuts of meat. The results are summarized in the table below.

Preservative A Preservative B
Sample means 95.25 100.50
Sample standard deviation 13.45 10.55

29) The most accurate statement that can be made about the p-value for testing whether there is 29)
a difference in the population variances for preservatives A and B is:
A) p -value = 0.00 B) 0.01 < p -value < 0.05
C) p -value > 0.05 D) p -value < 0.01

THE NEXT QUESTION IS BASED ON THE FOLLOWING INFORMATION:

A manager is considering the purchase of new production equipment to improve the output of the plant. Suppose the
equipment from two suppliers is extensively tested in multiple production runs. A total of 20 runs are recorded on
Supplier A's equipment and another 15 runs are reported from Supplier B's equipment. The volume produced is
recorded for each of the 35 runs. The results are summarized in the table below.

Supplier A Supplier B
Sample means 110 125
Sample standard deviation 10 15

30) The value of the test statistic for determining if there is a difference in the population 30)
variances for Supplier A and B is equal to:
A) 2.25 B) 0.44 C) 0.67 D) 1.5

5
31) Consider a random sample of 25 observations of two variables x and y. The following summary
statistics are available: = 43.2, = 195.6, = 1357.2, = 1253.4, and

= 4843.6. Which of the following is the slope of the sample regression line?
A) 0.43
B) 54.85
C) 0.978
D) 3.57

32) A company wishes to evaluate the effectiveness of a marketing campaign. Seventy five percent of all
potential professors were reached in a focused advertising program. Twenty eight percent of those
contacted adopted the book while 8% of the adoptions came from professors who did not receive the
promotional material. Define the following events of interest:
A1 = Professor received advertising material
A2 = Professor did not receive advertising material
B1 = Professor adopts the book
B2 = Professor does not adopt the book

What is the probability that a professor who adopts the book received the advertising material?

A) 0.70
B) 0.534
C) 0.962
D) 0.913

33) What is the probability that a professor who adopts the book has not received the advertising
material?
A) 0.10
B) 0.087
C) 0.20
D) 0.06

34) Let X be a random variable with the following distribution:

x -10 -5 0 5 10
P(x) 0.1 0.3 0.1 0.3 0.2

What is the probability that X is farther than one standard deviation from the mean?
A) 0.2 B) 0.3 C) 0.8 D) 0.1

35) In a recent survey, 70% of human resource directors thought that it was very important for business
students to take a course in business ethics. For a sample of 12 human resource directors, what is the
probability that at least one of them does not think it very important for business students to take a
business ethics course?
A) 0.9833 B) 0.9521 C) 0.9862 D) 0.9714

36) A very large logging operation has serious problems keeping their skidders operating properly. The
equipment fails at the rate of 3 breakdowns every 48 hours. Assume that x is time between breakdowns
and is exponentially distributed. The probability of a single breakdown within 24 hours is:
A) 0.0498 B) 0.7769 C) 0.2231 D) 0.9502

37) Suppose that x1 and x2 are random samples of observations from a population with mean μ and
variance σ2. Consider the following three point estimators, W, X, Y, and Z, of μ: W= (x1+ x2)/1.5, X = (x1

6
+ x2)/2, Y = (x1 + 3x2)/4, and Z = (x1 + 2x2)/3. Which of the estimators W, X, Y, and Z is the most
efficient?

A) W B) X C) Y D) Z

38) A professor of statistics wants to test that the average amount of money a typical college student
spends per day during spring break is over $70. Based upon previous research, the population standard
deviation is estimated to be $17.32. The professor surveys 35 students and finds that the mean spending
is $72.43. Which of the following statements is most accurate?
A) fail to reject the null hypothesis at α ≤ 0.10
B) reject the null hypothesis at α = 0.10
C) reject the null hypothesis at α = 0.05
D) reject the null hypothesis at α = 0.01

39) Suppose you have the following null and alternative hypotheses: H0 : σ2 = 34.5 and H1 : σ2 > 34.5. If
you take a random sample of 15 observations from a normally distributed population and find that s2 =
48.1, what is the most accurate statement that can be made about the p-value for this test?
A) 0.01 < p-value < 0.025
B) 0.025 < p-value < 0.05
C) 0.10 < p-value
D) 0.05 < p-value < 0.10

40) Thomas is a shift manager at a local fast food place, and is responsible for quality management.
Thomas wants to ensure that all the frozen hamburger patties that get delivered by the supplier weigh
four ounces on average. Assume that the standard deviation of the weight of hamburger patties is known
to be 0.1 ounces. Thomas tells one of his employees that as a shipment arrives, select 25 patties at
random and find the average weight for the 25 patties. For what average weight would you tell the
employee to reject the shipment, if you wanted the probability of a Type I error to be 0.10 or less?

A) 3.8926 B) 3.9744 C) 4.0330 D) 4.1247