Business Research Methods

You are choosing what to do on a summer day. There is a 20% chance you will go boating all day. There is a 25% chance you will go shopping all day. "Boat all day" and "shop all day" are A. Independent B. Dependent

B. Dependent

True or False: 5 out of every 10 coin flips will result in "Tails" A. TRUE B. FALSE

B. FALSE

True or False: There will be exactly 40 1's in any list of 400 digits from the table of random digits. A. TRUE B. FALSE

B. False

True or False: One should never trust the results of simulations for complex events, such as computing the probability of bridge failure. TRUE FALSE

FALSE

True or False: It is plausible that coin flips are independent. TRUE FALSE

TRUE

The more ____ the outcomes, the more trials are needed to ensure that the mean outcome is close to the expected value

variable

True or False: A personal probability is a number between 0 and 1.

True

____ of a statistic is the distribution of values taken by the statistic in all possible samples of the same size from the same population.

sampling distribution

____ of a statistic tells us what values the statistic takes in repeated samples from the same population and how often it takes those values

sampling distribution

Using random digits from a table or from computer software to imitate chance behavior is called ____.

simulation

____ is an interval calculated from sample data by a process that is guaranteed to capture the true population parameter in 95% of all samples

95% confidence interval

Computer voice recognition software is getting better. Some companies claim that their software correctly recognizes 98% of all words spoken by a trained user. To simulate recognizing a single word when the probability of being correct is 0.98, you could use random digits as follows: A) Two digits simulate one word; 00 to 97 mean "correct." B) Two digits simulate one word; 00 to 98 mean "correct." C) One digit simulates one word; 0 to 9 mean "correct." D) Three digits simulate one word; 001 to 098 mean "correct."

A) Two digits simulate one word; 00 to 97 mean "correct."

You read in a book about bridge that the probability that each of the four players is dealt exactly one ace is about 0.11. To simulate an outcome with probability 0.11 you could: A) look at two digits in the random number table; the outcome occurs if the digits are 11. B) look at two digits in the random number table; the outcome occurs if the digits are any of 00, 01, ... , 11. C) look at two digits in the random number table; the outcome occurs if the digits are any of 00, 01, ... , 10. D) look at two digits in the random number table; the outcome occurs if the digits are any of 01, 02, ... , 11. E) Both (C) and (D) are correct simulations.

A) look at two digits in the random number table; the outcome occurs if the digits are 11.

A female college student decides which party to attend based on the chances of a particular handsome male being present. She computed A. A personal probability B. The chances she would see the handsome male if she could repeat this night many times C. The probability of seeing the handsome male

A. A personal probability

_________ Is Unpredictable in the short run but has a regular and predictable pattern in the long run A. Chance Behavior B. Personal Probability C. Probability D. Law of Averages

A. Chance Behavior

The sampling distribution of a statistic A. Describes all possible values of the statistic and how often they will occur B. Is how we distribute our resources in sampling to get an accurate statistic C. Is the margin of error for the statistic

A. Describes all possible values of the statistic and how often they will occur

One might use simulation to compute a probability when A. The events are complex B. We do not know the probability model C. We do not have random digits D. There is a lot of time for computations

A. The events are complex

True or False: The general population think an event is more risky than it actually is when they feel they have very little control. A. TRUE B. FALSE

A. True

The approximate proportion of times a random outcome happens in a long series of repetitions is A.Its probability B. Its odds C. Unpredictable

A.Its probability

A poker player is dealt poor hands for several hours. He decides to bet heavily on the last hand of the evening on the grounds that after many bad hands he is due for a winner. A) He's right, because the winnings have to average out. B) He's wrong, because successive deals are independent of each other. C) He's right, because successive deals are independent of each other. D) He's wrong, because his expected winnings are $0 and he's below that now.

B) He's wrong, because successive deals are independent of each other.

Identify the legitimate assignment of probabilities for a sample space with 4 outcomes A.0.3, -0.1, 0.4, 0.4 B. 0.3, 0.3, 0.3, 0.1 C. 0.3, 0.4, 0.4, 0.4 D. 0.2, 0.2, 0.2, 0.2

B. 0.3, 0.3, 0.3, 0.1

What is the probability of "rolling a 7" when rolling 2 dice (that is, the sum of two dice is 7)? A. 6/7 B. 1/6 C. 1/36 D. 7/36

B. 1/6

What is the probability of rolling a 1 or a 2 when rolling a die? A. 1/6 B. 2/6 C. 3/6

B. 2/6

A correct interpretation of the law of averages is A. If I roll a die 600 times, I can predict 100 2's. B. If I roll a die many times, I can predict about 1/6 of the rolls to result in a 2. C. On average, half my dice rolls should result in a 2

B. If I roll a die many times, I can predict about 1/6 of the rolls to result in a 2.

____ of an outcome is a number between 0 and ! that express an individual's judgement of how likely the outcome is. A. Chance Behavior B. Personal Probability C. Probability D. Law of Averages

B. Personal Probability

Which of the following statements about a table of random digits is true? A) If each line contains 40 digits, there will be exactly 4 zeros in every line. B) The probability that there are exactly 4 zeros in a line of 40 digits is exactly 0.5. C) The expected number of zeros in a line of 40 digits is 4. D) There can never be 4 zeros in a row because that pattern isn't random. E) Both (C) and (D) are true.

C) The expected number of zeros in a line of 40 digits is 4.

Dr. Stats plans to toss a fair coin 10000 times in the hope that it will lead him to a deeper understanding of the laws of probability. Which of the following statements is true? A) It is unlikely that Dr. Stats will get more than 5000 heads. B) Whenever Dr. Stats gets a string of 15 tails in a row, it becomes more likely that the next toss will be a head. C) The fraction of tosses resulting in heads should be close to 1/2. D) The chance that the 100th toss will be a head depends somewhat on the results of the first 99 tosses. E) All of the above statements are true.

C) The fraction of tosses resulting in heads should be close to 1/2.

Suppose the sample proportion of those who will mainly use the internet to shop varies according to a normal distribution with mean, 0.45, and standard deviation 0.05. What percent of samples will indicate the proportion who will mainly internet shop is between 0.35 and 0.55? A. 16% B. 68% C. 95% D. 99.7%

C. 95%

The value z* for 99% confidence is 2.58. The 2.58 means A. The statistic is within 2.58% of the parameter B. The parameter will be in the interval 5.16% of the time C. 99% of the data in the normal distribution is within 2.58 standard deviations of the mean

C. 99% of the data in the normal distribution is within 2.58 standard deviations of the mean

The ______________ ,used to calculate a confidence interval, tells us how often the interval would contain the parameter if many samples were taken. A. Margin of error B. Statistic C. Confidence level

C. Confidence level

___ is a number between 0 & 1 that describes the proportion of times the outcome would occur in a very long series of repetitions A. Chance Behavior B. Personal Probability C. Probability D. Law of Averages

C. Probability

We call a phenomenon ____ if individuals outcomes are uncertain but there is nonetheless regular distribution of outcomes in a large number of repetitions A. Chance Behavior B. Personal Probability C. Random D. Law of Averages

C. Random

The probability of a random outcome is A. Unpredictable B. 1/2 C. Some number between 0 and 1

C. Some number between 0 and 1

A probability of 1 can be interpreted to mean A. The event has a 0.01% chance of happening B. The event has a 1% chance of happening C. The event has a 100% chance of happening

C. The event has a 100% chance of happening

The total area under any density curve A. Varies from sample to sample B. Is described by the margin of error C. Is either 68, 95, or 99.7% D. Equals 1

D. Equals 1

A random outcome A. Has a predictable pattern in the short term B. Has a 50/50 chance of occurrence C. Is haphazard D. Has a predictable pattern in the long term

D. Has a predictable pattern in the long term

in a large number of independent repetitions of a random phenomenon (like coin tossing) averages or proportions are likely to become more stable as the # of trails increase. A. Chance Behavior B. Personal Probability C. Probability D. Law of Averages

D. Law of Averages

A probability model can be described by A. Assigning probabilities to each individual outcome B.The margin of error C.A density curve D.Both (A) and (B) E. Both (A) and (C)

E. Both (A) and (C)

An ____ is an average of the possible outcomes in which each outcome is weighted by its probability, so that outcomes that occur more often get higher weights.

Expected value

True or False: Simulation uses random digits so one can only simulate independent events. TRUE FALSE

FALSE

____ draws conclusions about a population on the basis of data about a sample

Statistical inference

A remarkable statistical fact, called the _____ says that as we take more and more observations at random from any population, the distribution of the mean of these observations eventually gets close to a Normal distribution.

central limit theorem

A ______, which gives the probability that the interval will capture the true parameter value in repeated samples.

confidence level C

We sometimes call a collection of outcomes an ___.

event

The ___ of a random phenomenon that has numerical outcomes is found by multiplying each outcome by its probability and then adding all the products

expected value

The proportion of repetitions on which an event occurs will eventually be close to its probability, so simulation can ______.

give good estimates of probabilities.

Two random phenomena are ____ if knowing the outcome of one does not change the probabilities for outcomes of the other.

independent

According to the _____, if a random phenomenon with numerical outcomes is repeated many times independently, the mean of the actually observed outcomes approaches the expected value.

law of large numbers

The expected value calculated from a probability model really is the

long-run average

A ___ for a random phenomenon describes all the possible outcomes and says how to assign probabilities to any collection of outcomes.

probability model