University of Dubuque LIFE PROGRAM BAC 336: Introduction to Probability and Statistics Exam 1

    University of Dubuque
    LIFE PROGRAM
    BAC
    336: Introduction to Probability and Statistics Exam 1 true/FALSE.0001pt -40.5pt;”>_____
    1. The relative frequency approach to probability uses long term
    frequencies, often based on past data._____
    2. Predicting the outcome of a football game is using the subjective
    approach to probability._____
    3. You think you have a 90% chance of passing your next advanced
    financial accounting exam. This is an example of subjective approach to
    probability._____
    4. P(A)
    + P(B) = 1 for any events Aand Bthat are mutually
    exclusive._____
    5. The collection of all the possible outcomes of a random experiment
    is called a sample space._____
    6. The time required to drive from New York to New Mexico is a
    discrete random variable._____
    7. A random variable is a function or rule that assigns a number to
    each outcome of an experiment._____
    8. The number of home insurance policy holders is an example of a
    discrete random variable_____
    9. The mean of a discrete probability distribution for X is
    the sum of all possible values of X, divided by the number of possible
    values of X._____
    10. The length of time for which an apartment in a large complex
    remains vacant is a discrete random variable._____
    11. Since there is an infinite number of values a continuous random
    variable can assume, the probability of each individual value is virtually 0._____
    12. A continuous probability distribution represents a random variable
    having an infinite number of outcomes which may assume any number of values
    within an interval._____
    13. Continuous probability distributions describe probabilities
    associated with random variables that are able to assume any finite number of
    values along an interval._____
    14. A continuous random variable X has a uniform distribution between
    10 and 20 (inclusive), then the probability that X falls between 12 and
    15 is 0.30._____
    15. A continuous random variable is one that can assume an uncountable
    number of values._____
    16. The Central Limit Theorem permits us to draw conclusions about a
    population based on a sample alone, without having any knowledge about the
    distribution of that population. And this works no matter what the sample size
    is._____
    17. When a great many simple random samples of size nare drawn
    from a population that is normally distributed, the sampling distribution of
    the sample mean is normal regardless of the sample size n._____
    18. Consider an infinite population with a mean of 100 and a standard
    deviation of 20. A random sample of size 64 is taken from this population. The
    standard deviation of the sample mean equals 2.50._____
    19. If all possible samples of size n are drawn from an
    infinite population with standard deviation 8, then the standard error of the
    sample mean equals 1.0 if the sample size is 64._____
    20. A sample of size nis selected at random from an infinite
    population. As n increases, the standard error of the sample mean
    increases._____
    21. An unbiased estimator is said to be consistent if the difference
    between the estimator and the parameter grows smaller as the sample size grows
    larger._____
    22. An unbiased estimator is a sample statistic whose expected value
    equals the population parameter._____
    23. An unbiased estimator is said to be consistent if the difference
    between the estimator and the parameter grows larger as the sample size grows
    larger._____
    24. If there are two unbiased estimators of a parameter, the one whose
    variance is smaller is said to be relatively efficient._____
    25. An interval estimate is a range of values within which the actual
    value of the population parameter, such asm, may fall.MULTIPLE CHOICE_____ 26. Of the last 500 customers entering a
    supermarket, 50 have purchased a wireless phone. If the relative frequency
    approach for assigning probabilities is used, the probability that the next
    customer will purchase a wireless phone is

    a.

    0.10

    b.

    0.90

    c.

    0.50

    d.

    None of these choices.

    _____ 27. If you roll a balanced die 50 times, you
    should expect an even number to appear:

    a.

    on every other roll.

    b.

    exactly 50 times out of 100 rolls.

    c.

    25 times on average, over the long term.

    d.

    All of these choices are true.

    _____ 28. The collection of all possible outcomes of an
    experiment is called:

    a.

    a simple event

    b.

    a sample space

    c.

    a sample

    d.

    a population

    _____ 29. A sample space of an experiment consists of
    the following outcomes: 1, 2, 3, 4, and 5. Which of the following is a simple
    event?

    a.

    At least 3

    b.

    At most 2

    c.

    3

    d.

    15

    _____ 30. If two events are mutually exclusive, what is
    the probability that both occur at the same time?

    a.

    0.00

    b.

    0.50

    c.

    1.00

    d.

    Cannot be determined from the information
    given.

    _____ 31. A table, formula, or graph that shows all
    possible values a random variable can assume, together with their associated
    probabilities, is called a(n):

    a.

    discrete probability distribution.

    b.

    discrete random variable.

    c.

    expected value of a discrete random
    variable.

    d.

    None of these choices.

    _____ 32. A function or rule that assigns a numerical
    value to each simple event of an experiment is called:

    a.

    a sample space.

    b.

    a probability distribution.

    c.

    a random variable.

    d.

    None of these choices.

    _____ 33. A lab at the DeBakey Institute orders 150
    rats a week for each of the 52 weeks in the year for experiments that the lab
    conducts. Suppose the mean cost of rats used in lab experiments turned out to be
    $20.00 per week. Interpret this value.

    a.

    Most of the weeks resulted in rat costs of
    $20.00

    b.

    The median cost for the distribution of rat
    costs is $20.00

    c.

    The expected or average costs for all
    weekly rat purchases is $20.00

    d.

    The rat cost that occurs more often than
    any other is $20.00

    _____ 34. In the notation below, X is the random
    variable, c is a constant, and V refers to the variance. Which of
    the following laws of variance is not true?

    a.

    V(c) = 0

    b.

    V(X + c) = V(X)
    + c

    c.

    V(cX) = c2 V(X)

    d.

    None of these choices.

    _____ 35. If n = 10 and p = 0.60, then
    the mean of the binomial distribution is

    a.

    0.06

    b.

    2.65

    c.

    6.00

    d.

    5.76

    _____ 36. 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.

    _____ 37. Which of the following is not a
    characteristic for a normal distribution?

    a.

    It is symmetrical.

    b.

    The mean is always zero.

    c.

    The mean, median, and mode are all equal.

    d.

    It is a bell-shaped distribution.

    _____ 38. 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

    _____ 39. What proportion of the data from a normal
    distribution is within two standard deviations from the mean?

    a.

    0.3413

    b.

    0.4772

    c.

    0.6826

    d.

    0.9544

    _____ 40. Given that Z is a standard normal
    variable, the variance of Z:

    a.

    is always greater than 2.0.

    b.

    is always greater than 1.0.

    c.

    is always equal to 1.0.

    d.

    cannot assume a specific value.

    _____ 41. The standard deviation of the sampling
    distribution of.gif”> is also called
    the:

    a.

    central limit theorem.

    b.

    population standard deviation.

    c.

    finite population correction factor.

    d.

    standard error of the sample mean.

    _____ 42. The finite population correction factor
    should be used:

    a.

    whenever we are sampling from an infinite
    population.

    b.

    whenever we are sampling from a finite
    population.

    c.

    whenever the sample size is large compared
    to the population size.

    d.

    whenever the sample size is small compared
    to the population size.

    _____ 43. If all possible samples of size n are
    drawn from an infinite population with a mean ofm and a standard deviation ofs, then the standard error of the sample mean
    is inversely proportional to:

    a.

    m

    b.

    s

    c.

    n

    d.

    .gif”>

    _____ 44. If a random sample of size nis drawn
    from a normal population, then the sampling distribution of the sample mean.gif”> will be:

    a.

    normal for all values of n.

    b.

    normal only for n > 30.

    c.

    approximately normal for all values of n.

    d.

    approximately normal only for n >
    30.

    _____ 45. If all possible samples of size n are
    drawn from a population, the probability distribution of the sample mean.gif”> is called the:

    a.

    standard error of.gif”>.

    b.

    expected value of.gif”>.

    c.

    sampling distribution of.gif”>.

    d.

    normal distribution.

    _____ 46. An estimator is said to be consistent if:

    a.

    the difference between the estimator and
    the population parameter grows smaller as the sample size grows larger.

    b.

    it is an unbiased estimator.

    c.

    the variance of the estimator is zero.

    d.

    the difference between the estimator and
    the population parameter stays the same as the sample size grows larger.

    _____ 47. A point estimator is defined as:

    a.

    a range of values that estimates an unknown
    population parameter.

    b.

    a single value that estimates an unknown
    population parameter.

    c.

    a range of values that estimates an unknown
    sample statistic.

    d.

    a single value that estimates an unknown
    sample statistic.

    _____ 48. An unbiased estimator of a population
    parameter is defined as:

    a.

    an estimator whose expected value is equal
    to the parameter.

    b.

    an estimator whose variance is equal to
    one.

    c.

    an estimator whose expected value is equal
    to zero.

    d.

    an estimator whose variance goes to zero as
    the sample size goes to infinity.

    _____ 49. The sample variance s2 is
    an unbiased estimator of the population variances2 when the denominator of s2
    is

    a.

    n + 1

    b.

    n

    c.

    n- 1

    d.

    .gif”>

    _____ 50. Which of the following would be an
    appropriate null hypothesis?

    a.

    The population proportion is equal to 0.60.

    b.

    The sample proportion is equal to 0.60.

    c.

    The population proportion is not equal to
    0.60.

    d.

    All of these choices are true.

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