Deck 9: Using Probability to Make Decisions About Data

Question 1

Which of the following best describes knowing the relative frequency of every possible event in a population?

A)A probability distribution
B)A population distribution
C)A frequency distribution
D)A sample distribution

Answer 1

A probability distribution

Question 2

Two events are said to be independent when

A)the probability of one event is influenced by the occurrence of the other event.
B)you do not have knowledge about the occurrence of either event.
C)the probability of one event is determined by the occurrence of the other event.
D)the probability of one event is not influenced by the occurrence of the other event.

Answer 2

the probability of one event is not influenced by the occurrence of the other event.

Question 3

The probability of getting heads on a fair coin is 0.50.The probability of getting tails is also 0.50.If you toss the coin three times and get heads all three times,what is the probability of getting tails on the next toss?

A)0.25
B)0.75
C)0.50
D)0.30

Answer 3

0.50

Question 4

You roll a die (the singular of dice)twice,and both times you roll a 6.What type of events are these two rolls?

A)Biased
B)Dependent
C)Independent
D)Likely

Question 5

On a roll of a die,the probability that 3 or more dots will appear on the top side is 0.67,and the probability that 2 or fewer dots will appear is 0.33.If we know that 6 dots showed up on the last throw,what is the probability that 2 or 1 will show up on the next throw?

A)1.00
B)0.83
C)0.33
D)0.17

Question 6

A probability distribution gives us

A)a distribution of probabilities.
B)the probability of every possible event in a population.
C)the probability of some of the events in the population.
D)the probability of obtaining certain probabilities.

Question 7

The president of State College wants to conduct a survey of the students.He knows there are 325 freshmen,250 sophomores,175 juniors,100 seniors,and 150 graduate students.What is the probability that the very first person randomly selected for the survey will be a freshman?

A)0.03
B)0.01
C)0.33
D)0.60

Question 8

The purpose of probability and inferential statistics is to

A)infer exact values for the population.
B)make statements with certainty about characteristics of the population.
C)perform studies on an entire population.
D)make decisions about whether the relationship seen in a sample would be found in the population..

Question 9

An event's relative frequency in the population equals

A)100%.
B)the average number of times an event occurs in the population.
C)the odds of the event.
D)the probability of the event.

Question 10

One hundred lottery tickets have been sold.You've purchased 30 tickets.What is the probability of one of your tickets being randomly selected?

A)0.03
B)0.01
C)0.30
D)0.60

Question 11

Which of the following accurately describes an empirical probability distribution? It is based on

A)a theoretical model of the relative frequency of events in a population.
B)the assumption the relative frequencies from observed samples represent those in the population.
C)determining the relative frequencies of all events in a population.
D)determining the relative frequencies of all events in a sampling distribution.

Question 12

When we select a sample so that all elements in the population have an equal chance of being selected,we are using

A)inferential statistics.
B)random sampling.
C)probability.
D)dependent events.

Question 13

Suppose you select a candy from a jar with 6 red and 4 green candies.You draw out a red candy,unwrap it,and eat it.You then select a second candy from the jar.What is the probability you draw out a green candy this time?

A)0.44
B)0.40
C)0.60
D)0.56

Question 14

As a general rule,when statisticians determine the probability of events,they assume that the events are _____ and sampled _____ replacement.

A)independent;with
B)independent;without
C)dependent;with
D)dependent;without

Question 15

Suppose you take a piece of candy out of a jar,look to determine its color,then put it back into the jar before you randomly select the next piece of candy.This type of sampling is called

A)an independent event.
B)sampling with replacement.
C)a dependent event.
D)sampling without replacement.

Question 16

Asaad wants to show Cheryl and Cindy a card trick he has learned.He first asks Cheryl to draw one card at random from a standard deck of 52 cards.Cheryl draws out the 4 of hearts,shows the card to Cindy,and then lays it face down on the table in front of her.Asaad then extends the remaining cards for Cindy to make her selection.What is the probability that Cindy also will draw out a heart?

A)0.25
B)0.24
C)0.02
D)0.20

Question 17

Suppose you select a candy from a jar with 6 red and 4 green candies,note its color,and then replace it ten times.Each time,the candy you have selected has been green.What is the probability that on the next drawing you will select a red candy?

A)1.0
B)0.48
C)0.90
D)0.60

Question 18

There are 26 red cards in a playing deck and 26 black cards.The probability of randomly selecting a red card or a black card is 26/52 = 0.50.Suppose you randomly select a card from the deck five times,each time replacing the card and reshuffling before the next pick.Each of the five selections has resulted in a red card.On the sixth turn,the probability of getting a black card

A)has got to be low because you've gotten so many red cards on the previous turns.
B)has got to be high because you've gotten so many red cards on the previous turns.
C)is the same as it has always been if the deck is a fair deck.
D)needs to be recomputed because you are sampling with replacement.

Question 19

Which of the following accurately describes a theoretical probability distribution? It is based on

A)a theoretical model of the relative frequency of events in a population.
B)a theoretical model of the relative frequency of events in a sample.
C)the assumption the relative frequencies from observed samples represent those in the population.
D)determining the relative frequencies of some of the events in a sampling distribution.

Question 20

How is the relative frequency of an event defined?

A)The proportion of time an event does not occur in the population of events.
B)The average number of time an event occurs in the population of events.
C)The proportion of time an event occurs out of all events that might occur in the population.
D)The proportion of time all events occur.

Question 21

When a sample mean is different from the mean of the sampling distribution (the population mean),two alternatives must be considered: The sample mean may represent _____,or it may represent _____.

A)the central tendency of a population well;the variability of a population well
B)a well population;a poor population
C)the population poorly;the population well
D)the population poorly;a different population

Question 22

What can we conclude about a sample mean that is found to lie in the region of rejection? It is extremely _____ to have occurred by chance,and it represents _____.

A)unlikely;the population
B)likely;the population
C)unlikely;some other population
D)likely;some other population

Question 23

Which of the following is correct regarding means that fall within the region of rejection when the critical values are ?

A)It is likely they represent the population under study.
B)They have a high relative frequency.
C)They occur with a probability of 95%.
D)They occur with a probability of 5%.

Question 24

Which of the following is the criterion that psychologists usually use to determine the likelihood that a sample mean was obtained by chance?

A)p = 0.005
B)p = 0.05
C)p = 0.50
D)p = 0.01

Question 25

_____ occurs when random chance produces a sample statistic that is not equal to the population parameter it represents.

A)Random sampling
B)Sampling error
C)Criterion probability
D)Sampling replacement

Question 26

What do we call that portion of the sampling distribution in which values are considered too unlikely to have occurred by chance?

A)Region of criterion value
B)Region of critical value
C)Region of rejection
D)Critical value

Question 27

An advertising executive wanted to know whether a new ad campaign designed to deter children from smoking was working.After seeing the ads,a randomly selected sample of 36 teenagers rated what they thought of smoking on a -5 (it's terrible)to +5 (it's fantastic).The mean rating for the sample was -0.70.The population mean is 0,with a population standard deviation of 2.00.What is the probability of obtaining a sample mean of -0.70 or lower (more negative)?

A)0.0179
B)0.1368
C)0.3632
D)0.4821

Question 28

A student wanted to know whether memory for items on a grocery list was better when a bizarre image was created for each item,compared with a strategy of simply trying to remember the items.The student had a randomly selected sample use bizarre imagery to remember a list of 15 items;the mean number of items remembered was 10.The student compared this mean to a population mean of 7 and a standard error of 1.20.What is the probability of obtaining a sample mean of 10 or higher?

A)0.0062
B)0.1151
C)0.4938
D)0.9938

Question 29

When rolling a pair of fair dice,the probability of rolling a total point value of "7" is 0.17.If you rolled a pair of dice 1,000 times and the point value of "7" appeared 723 times,what would you probably conclude?

A)This is not so unlikely as to make you doubt the fairness of the dice.
B)Although not impossible,this outcome is so unlikely that the fairness of these dice is questionable.
C)Since the total point value of "7" has the highest probability of any event in the sampling distribution,this is an extremely likely outcome.
D)It is impossible for this to happen if the dice are fair.

Question 30

What is the purpose of the critical value?

A)To determine the size of the region of rejection.
B)To determine the maximum allowable population standard deviation
C)To determine the likelihood that the population mean was obtained by chance
D)To determine the value of z needed to conclude that the population mean was obtained by chance

Question 31

The criterion determines

A)the critical value of the sample mean.
B)the probability of the sample mean.
C)the standard deviation (standard error)of the sampling distribution of means.
D)the size of the region of rejection.

Question 32

What is the critical value?

A)The outer end of the region of rejection
B)The inner edge of the region of rejection
C)The absolute value of the entire region of rejection
D)The value of z needed to conclude that the population mean occurred by chance

Question 33

The scores that lie in the tails of a normal distribution have a _____ frequency and a _____ probability of occurring.

A)high;high
B)low;high
C)high;low
D)low;low

Question 34

Why can we never be sure that a sample represents a population?

A)Random selection never works the way it is supposed to work.
B)Samples created by random selection are almost never perfectly representative.
C)A random sample may poorly represent a population,or it may accurately represent a different population.
D)If selection is conducted correctly,samples always accurately represent the populations they are supposed to represent.

Question 35

What is the probability of getting a sample mean between 500 and 520 if the population mean is 500 and the standard deviation of the sampling distribution (the standard error of the mean)is 20?

A)0.5000
B)0.4332
C)0.3413
D)0.1915

Question 36

If the probability of getting a z-score between the mean and +1 standard deviation is 0.3413,what is the probability of getting a z-score lower than -1 standard deviation?

A)0.3413
B)0.1587
C)0.6587
D)0.8413

Question 37

We create the sampling distribution of means from

A)a random sample of all possible means.
B)the region of rejection.
C)the z-distribution.
D)the underlying raw score population.

Question 38

Which of the following is not true of the criterion?

A)The criterion is the probability that defines samples as unlikely.
B)Samples that meet the criterion occur more than 5% of the time.
C)Behavioral researchers usually use 0.05 as their criterion probability.
D)Sample means that occur with a probability less than that of the criterion probability are likely to represent some other population.

Question 39

If the probability of getting a z-score between the mean and +1 standard deviation is 0.3413,what is the probability of getting a z-score of +1 standard deviation or less?

A)0.3413
B)0.1587
C)0.6587
D)0.8413

Question 40

Your professor told the class that,typically,20% of the class receives As,20% Bs,35% Cs,10% Ds,and 15% Fs.What is the probability that the student sitting next to you will receive an A or an F?

A)0.35
B)0.50
C)35%
D)65%

Question 41

What can you conclude about a sample mean that falls within the region of rejection?

A)The sample probably represents some population other than the one on which the sampling distribution was based.
B)The sample represents the population on which the sampling distribution was based.
C)Another sample needs to be collected.
D)The sample should have come from the given population.

Question 42

At a basic level,when deciding whether a sample is representative of a particular population,we

A)make the decision based on intuition.
B)are also deciding whether the population is the one we should be testing.
C)decide against low-probability events in favor of high-probability events.
D)go for the long shot and decide against high-probability events.

Question 43

A study about the college aptitude of seniors at North City High School has resulted in a sample mean with a corresponding z-score of $\pm$ 2.00.If the critical value for the region of rejection is ,what is the correct conclusion?

A)Since the z-value falls within the region of rejection,we should conclude this sample mean likely represents some other population.
B)Since the z-value does not fall within the region of rejection,we should not conclude this sample mean represents some other population.
C)Since the z-value falls within the region of rejection,we should not conclude this sample mean represents some other population.
D)Since the z-value does not fall within the region of rejection,we should conclude this sample mean likely represents some other population.

Question 44

What can we conclude when the absolute value of a z-score for a sample mean is larger than the critical value?

A)The random selection procedure was conducted improperly.
B)The sample mean is reasonably likely to have come from the given population by random sampling.
C)The sample mean represents the particular raw score population on which the sampling distribution is based.
D)The sample mean does not represent the particular raw score population on which the sampling distribution is based.

Question 45

Suppose you drew a random sample from a population where the mean is 100.The standard error of the sampling distribution is 10.The mean for your sample is 80.What could you conclude about your sample?

A)The sample mean does not occur very often by chance in the sampling distribution of means and probably did not come from the given population.
B)The sample mean occurs very often by chance in the sampling distribution of means and probably did not come from the given population.
C)The sample mean does not occur very often by chance in the sampling distribution of means but probably did come from the given population.
D)The sample mean occurs very often by chance in the sampling distribution of means and probably did come from the given population.

Question 46

A cognitive psychologist tested whether people spend more time looking at and comprehending content words (e.g. ,ball,kick)than other words (the,a)when reading a passage.The mean looking time for a sample of content words was compared to the mean looking time for the population of other words by transforming it into a z-score.The z-score for the sample mean was z = 3.00.With critical values of $\pm$ 1.96,what should the psychologist conclude about the sample mean?

A)It is an unlikely sample for the population of looking times for other words and probably represents some other population (looking times for meaningful words).
B)Because of chance,the sample simply represents the population of looking times for other words poorly.
C)Because of chance,the sample probably represents some other population (looking times for meaningful words).
D)It is an unlikely sample for the population of looking times for other words,but it simply represents the population poorly.

Question 47

When +1.645 is used as the critical value instead of ±1.96,

A)the total probability of the region of rejection is decreased.
B)the total probability of the region of rejection is increased.
C)the region of rejection is all placed in the positive tail.
D)the region of rejection is all placed in the negative tail.

Question 48

A study about the college aptitude of seniors at South City High School has resulted in a sample mean with a corresponding z-score of +1.89.If the critical value for the region of rejection is ,what is the correct conclusion?

A)Since the z-value falls within the region of rejection,we should conclude this sample mean likely represents some other population.
B)Since the z-value does not fall within the region of rejection,we should not conclude this sample mean represents some other population.
C)Since the z-value falls within the region of rejection,we should not conclude this sample mean represents some other population.
D)Since the z-value does not fall within the region of rejection,we should conclude this sample mean likely represents some other population.

Question 49

Suppose you drew a random sample from a population where the mean is 100.The standard error of the sampling distribution is 10.The mean for your sample is 110.What could you conclude about your sample?

A)The sample mean does not occur very often by chance in the sampling distribution of means and probably did not come from the given population.
B)The sample mean occurs quite often by chance in the sampling distribution of means and probably did not come from the given population.
C)The sample mean does not occur very often by chance in the sampling distribution of means but probably did come from the given population.
D)The sample mean occurs very often by chance in the sampling distribution of means and probably did come from the given population.

Question 50

The mean of the population ( )is 200 on a test that measures math skills of middle school students.The variance .The test scores for the students in Mr.Petris's class at Suburban Middle School are given below.Use a rejection region with a probability of 5% only in the upper tail.What should you conclude?

A)Since the z-value falls within the region of rejection,we should conclude this sample mean likely represents some other population.
B)Since the z-value does not fall within the region of rejection,we should not conclude this sample mean represents some other population.
C)Since the z-value falls within the region of rejection,we should not conclude this sample mean represents some other population.
D)Since the z-value does not fall within the region of rejection,we should conclude this sample mean likely represents some other population.

Question 51

How can we determine the representativeness of a sample mean for a particular population?

A)Draw a graph and compare the heights of the bars representing the population and sample means.
B)Convert the sample mean to a z-score and compare the z-score to the critical value.
C)Compare the sample mean to the population mean and compare the difference to the criterion.
D)Compare the sample mean to the population standard deviation and look up its probability.

Question 52

When a z-score is not in the region of rejection,we should

A)reject the idea that random chance produced a sample that represents the population poorly.
B)conclude with the idea that the sample scores and the raw score population are similar enough to be called identical.
C)not reject the idea that the sample represents the raw score population.
D)reject the idea that the sample represents the raw score population.

Question 53

If we decide not to reject the idea that a sample represents a particular population,because the sample mean does not lie within the rejection region,

A)although the probability is low,our decision may be wrong.
B)the probability is high that our decision is wrong.
C)we cannot know the probability of our decision being right or wrong.
D)the probability of our decision being correct is 0.05.

Question 54

In a test of physical fitness,a group of men ages 65 and older from a local retirement community were told to do as many sit-ups as they could.It is known that the population mean is 20 with .The scores for the men from the retirement community are given below.Use a two-tailed rejection region with a total area of 0.05.What should you conclude?

A)Since the z-value falls within the region of rejection,we should conclude this sample mean likely represents some other population.
B)Since the z-value does not fall within the region of rejection,we should not conclude this sample mean represents some other population.
C)Since the z-value falls within the region of rejection,we should not conclude this sample mean represents some other population.
D)Since the z-value does not fall within the region of rejection,we should conclude this sample mean likely represents some other population.

Question 55

The introductory biology class at State University is conducting a study of water quality in their local community.The population mean of a certain beneficial bacteria found in drinking water ( )is 100,with .The bacteria counts from the community are given below.Use a two-tailed rejection region with a total area of 0.05.What should you conclude?

A)Since the z-value falls within the region of rejection,we should conclude this sample mean likely represents some other population.
B)Since the z-value does not fall within the region of rejection,we should not conclude this sample mean represents some other population.
C)Since the z-value falls within the region of rejection,we should not conclude this sample mean represents some other population.
D)Since the z-value does not fall within the region of rejection,we should conclude this sample mean likely represents some other population.

Question 56

If we decide to reject the idea that a sample represents a particular population,because the sample mean lies within the region of rejection,

A)although the probability is low,our decision may be wrong.
B)the probability is high that our decision is wrong.
C)we cannot know the probability of our decision being wrong.
D)the probability of our decision being correct is 0.05.