Assignment 4 (mostly Chapter 7)

Multiple Choice

1. Convenience sampling is an example of

            a.          probabilistic sampling

            b.         stratified sampling

            c.          nonprobabilistic sampling

            d.         cluster sampling

2. Cluster sampling is

            a.          a nonprobability sampling method

            b.         the same as convenience sampling

            c.          a probability sampling method

            d.         None of these alternatives is correct.

3. The closer the sample mean is to the population mean,

            a.          the larger the sampling error

            b.         the smaller the sampling error

            c.          the sampling error equals 1

            d.         None of these alternatives is correct.

4. Since the sample size is always smaller than the size of the population, the sample mean

            a.          must always be smaller than the population mean

            b.         must be larger than the population mean

            c.          must be equal to the population mean

            d.         can be smaller, larger, or equal to the population mean

5. As the sample size increases, the

            a.          standard deviation of the population decreases

            b.         population mean increases

            c.          standard error of the mean decreases

            d.         standard error of the mean increases

6. A simple random sample from an infinite population is a sample selected such that

            a.          each element is selected independently and from the same population

            b.         each element has a 0.5 probability of being selected

            c.          each element has a probability of at least 0.5 of being selected

            d.         the probability of being selected changes

7. If we consider the simple random sampling process as an experiment, the sample mean is

            a.          always zero

            b.         always smaller than the population mean

            c.          a random variable

            d.         exactly equal to the population mean

8. A population has a mean of 75 and a standard deviation of 8.  A random sample of 800 is selected.  The expected value of x(bar) is

            a.          8

            b.         75

            c.          800

            d.         None of these alternatives is correct.

9. As the sample size becomes larger, the sampling distribution of the sample mean approaches a

            a.          binomial distribution

            b.         Poisson distribution

            c.          normal distribution

            d.         chi-square distribution

10. The purpose of statistical inference is to provide information about the

            a.          sample based upon information contained in the population

            b.         population based upon information contained in the sample

            c.          population based upon information contained in the population

            d.         mean of the sample based upon the mean of the population

11. A simple random sample of 64 observations was taken from a large population.  The sample mean and the standard deviation were determined to be 320 and 120 respectively.  The standard error of the mean is

            a.          1.875

            b.         40

            c.          5

            d.         15

12. A population has a mean of 80 and a standard deviation of 7.  A sample of 49 observations will be taken.  The probability that the sample mean will be larger than 82 is

            a.          0.5228

            b.         0.9772

            c.          0.0228  

            d.         0.4772

13. There are 7 children in a family.  The number of children defines a population.  The number of simple random samples of size 2 (without replacement) which are possible equals

            a.          12

            b.         15

            c.          3

            d.         21

14. Four hundred people were asked whether gun laws should be more stringent.  Three hundred said “yes,” and 100 said “no.”  The point estimate of the proportion in the population who will respond “yes” is

            a.          300

            b.         approximately 300

            c.          0.75

            d.         0.25

15. The sampling distribution of the sample means

            a.          is the probability distribution showing all possible values of the sample mean

            b.         is used as a point estimator of the population mean m

            c.          is an unbiased estimator

            d.         shows the distribution of all possible values of m

Problem 1

Business Week surveyed MBA alumni 10 years after graduation.  One finding was that alumni spend an average of $115.50 per week eating out socially.  You have been asked to conduct a follow-up study by taking a sample of 40 of these MBA alumni.  Assume the population standard deviation is $35.

16. What is the standard error of the mean? (round to 2 decimals)

17. What is the probability that the sample mean will be within $10 of the population mean? (4 decimals)

18. Suppose you find a sample mean of $100.  What is the probability of finding a sample mean of $100 or less? (4 decimals)

19. Would you consider this sample to be an unusually low spending group of alumni?

            a. Yes, given the probability found in the question above is relatively high.

            b. Yes, given the probability found in the question above is relatively low.

            c. No, given the probability found in the question above is relatively high.

            d. No, given the probability found in the question above is relatively low.

Problem 2

Money magazine reported that the average price of a gallon of gasoline in the U.S. during the first quarter of 2001 was $1.46.  Assume the price reported is the population mean and the population standard deviation is $0.15.

20. What is the probability that the mean price for a sample of 30 gas stations is within $0.03 of the population mean?

(4 decimals)

21. What is the probability that the mean price for a sample of 50 gas stations is within $0.03 of the population mean?

(4 decimals)

22. What is the probability that the mean price for a sample of 100 gas stations is within $0.03 of the population mean?

(4 decimals)

23. Would you recommend a sample size of 30, 50, or 100 to have at least a .95 probability that t sample mean is within $0.03 of the population mean? (answer either 30, 50, or 100)

Problem 3

The mean annual starting salary for marketing majors is $34,000.  Assume the standard deviation for this population is $2,000.

24. What is the probability that a simple random sample of 30 marketing majors will have a sample mean within +/-  $250 of the population mean? (4 decimals)

25. What is the probability that a simple random sample of 100 marketing majors will have a sample mean within +/-  $250 of the population mean? (4 decimals)

26. What is the probability that a simple random sample of 400 marketing majors will have a sample mean within +/-  $250 of the population mean? (4 decimals)

27. As the sample size increases

            a. the probability that the sample mean will be within a specified distance from the population mean increases.

            b. the probability that the sample mean will be within a specified distance from the population mean decreases.

            c. the probability that the sample mean will be within a specified distance from the population mean does not change.

            d. None of the above are correct.

Problem 4 (from second half of chapter 6)

The average amount parents and children spent per child on back-to-school clothes in Fall 2001 was $527.  Assume the standard deviation is $160 and that the amount spent is normally distributed.

28. What is the probability that the amount spent on a randomly selected child is more than $700? (4 decimals)

29. What is the probability that the amount spent on a randomly selected child is less than $100? (4 decimals)

30. What is the probability that the amount spent on a randomly selected child is between $450 and $700? (4 decimals)

31. What is the probability that the amount spent on a randomly selected child is no more than $300? (4 decimals)