# The relative frequency approach to probability

Question

TRUE/FALSE

_____ 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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