Practice Multiple Choice Questions for Exam 2

Prof. Alex Angelus

Sept. 20, 2014

2. Which of the following regarding the mean and variance of

a portfolio of two stocks is false?

a. .

b. . \

c.

d. .

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Question 1

Question 2

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2. Which of the following are required conditions for the

distribution of a discrete random variable X that can assume

values xi?

a. 0 p(xi) 1 for all xi

b.

c. Both a) and b) are required conditions

d. Neither a) nor b) are required conditions

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Question 3

3. Which of the following cannot have a Poisson distribution?

a. The length of a movie.

b. The number of telephone calls received by a switchboard in

a specified time period.

c. The number of customers arriving at a gas station in

Christmas day.

d. The number of bacteria found in a cubic yard of soil.

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Question 4

4. The Sutton police department must write, on average, 6

tickets a day to keep department revenues at budgeted levels. Suppose

the number of tickets written per day follows a Poisson distribution

with a mean of 6.5 tickets per day. Interpret the value of the mean.?

a. The mean has no interpretation.

b. The expected number of tickets written would be 6.5 per day.

c. Half of the days have less than 6.5 tickets written and half of the

days have more than 6.5 tickets written.

d. The number of tickets that is written most often is 6.5 tickets per

day.

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Question 5

5. Suppose f(x) = 0.25. What range of possible values can X

take on and still have the density function be legitimate?

a. [0, 4]

b. [4, 8]

c. [-2, +2]

d. All of these choices are true.

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Question 6

6. If the random variable X has a uniform distribution

between 40 and 50, then P(35 X 45) is:

a. 1.0

b. 0.5

c. 0.1

d. undefined.

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Question 7

7. If X has a normal distribution with mean 60 and

standard deviation 6, which value of X corresponds with

the value z = 1.96?

a. x = 71.76

b. x = 67.96

c. x = 61.96

d. x = 48.24

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Question 8

8. If two random samples of sizes n1 and n2 are selected

independently from two populations with variances

and , then the standard error of the sampling distribution

of the sample mean difference, , equals

a. .

b.

.

c.

d. .

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Question 9

9. Random samples of size 49 are taken from an infinite

population whose mean is 300 and standard deviation is 21.

The mean and standard error of the sample mean,

respectively, are:

a. 300 and 21

b. 300 and 3

c. 300 and 0.43

d. None of these choices.

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Question 10

10. If all possible samples of size n are drawn from an infinite

population with a mean of and a standard deviation of ,

then the standard error of the sample mean is inversely

proportional to:

a.

b.

c. n

d. n

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Question 11

11. Suppose that 100 items are drawn from a population of

manufactured products and the weight, X, of each item is

recorded. Prior experience has shown that the weight has a non-

normal probability distribution with = 8 ounces and = 3

ounces. Which of the following is true about the sampling of the

sample mean?

a. Its mean is 8 ounces.

b. Its standard error is 0.3 ounces.

c. Its shape is approximately normal.

d. All of these choices are true.

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Question 12

12. If two random samples of sizes n1 and n2 are selected

independently from two non-normally distributed populations,

then the sampling distribution of the sample mean difference is

a. Always non-normal

b. Approximately normal if one of the samples sizes is larger than

or equal to 30.

c. Approximately normal only if n1 and n2 are both larger than or

equal to 30

d. Approximately normal regardless of n1 and n2

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Question 13

13. If there are two unbiased estimators of a population parameter

available, the one that has the smallest variance is said to be:

a. a biased estimator.

b. relatively efficient.

c. consistent.

d. relatively unbiased.

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Question 14

14. The letter in the formula for constructing a confidence

interval estimate of the population mean is:

a. the level of confidence.

b. the probability that a particular confidence interval will

contain the population mean.

c. the area in the lower tail of the sampling distribution of the

sample mean.

d. None of these choices.

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Question 15

15. In developing an interval estimate for a population mean,

the population standard deviation was assumed to be 10. The

interval estimate was 50.92 2.14. Had the population

standard deviation equalled 20, the interval estimate would

have been

a. 60.92 2.14

b. 50.92 12.14

c. 101.84 4.28

d. 50.92 4.28

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Question 16

16. Which of the following statements is false regarding the

sample size needed to estimate a population mean?

a. It is directly proportional to the population variance.

b. It is directly proportional to the square of z+

c. It is directly proportional to the square of the maximum

allowable error B.

d. None of these choices.

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Question 17

17. Researchers claim that 40 tissues is the average number of

tissues a person uses during the course of a cold. The

company who makes Puffs brand tissues thinks that fewer of

their tissues are needed. What are their null and alternative

hypotheses?

a. H0: m = 40 vs. H1: m > 40 c. H0: = 40 vs. H1: < 40

b. H0: m = 40 vs. H1: m < 40 d. H0: m < 40 vs. H1: m = 40

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Question 18

18. The owner of a local Jazz Club has recently surveyed a

random sample of n = 200 customers of the club. She would

now like to determine whether or not the mean age of her

customers is over 30. If so, she plans to alter the entertainment

to appeal to an older crowd. If not, no entertainment changes

will be made. The appropriate hypotheses to test are:

a. H0: m = 30 vs. H1: m < 30. c. H0: = 30 vs. H1: < 30.

b. H0: m = 30 vs. H1: m > 30. d. H0: = 30 vs. H1: > 30.

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Question 19

19. In a two-tail test for the population mean, the null hypothesis

will be rejected at a level of significance if the value of the

standardized test statistic z is such that:

a. z > za

b. z < -za

c. -za < z < za

d. | z | > za / 2

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Question 20

20. If the value of the sample mean is close enough to the

hypothesized value 0 of the population mean , then:

a. the value of m0 is definitely correct.

b. the value of m0 is definitely wrong.

c. we reject the null hypothesis.

d. we cannot reject the null hypothesis.