chapter 8

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2. A random variable can be defined as: Multiple choice question. One from a set of variables representing different outcomes to a chance experiment Reason: One variable is used to represent all outcomes. a variable chosen by chance to represent the outcomes of an experiment Reason: It is the value, not the variable that is random. a quantity resulting from a random experiment that can have different values Choose the random variables from this set that are discrete. Select all that apply. Multiple select question. Number of drive-thru customers to the bank on a given day. The number of dots uppermost of rolling a pair of dice. The weight of a bag of a dozen apples. Reason: The bag can take on any weight over a given range, say 9 to 10 pounds. The travel time of an airline flight. Reason: The travel time can take on any value over a given range, say 1 to 2 hours. What shows the possible outcomes of a random experiment and the probability of each outcome? Multiple choice question. A Scatter Diagram Reason: A scatter diagram shows the relationship between two variables. See Chapter 4. A Random Number Table Reason: A random number table is just a listing of the digits 0-9 listed in random order. A Stem and Leaf Plot Reason:

This is a descriptive tool for displaying data. See Chapter 4. A Probability Distribution Choose the two random variables from this list that are continuous. Multiple select question. The average temperature in NYC during May. The number of apples per bag in a supermarket. Reason: This random variable can assume only certain clearly separated values. The number of ads during a television show. Reason: This random variable can assume only certain clearly separated values. The wait time at the dentist. Choose the statements that describe characteristics of a Probability Distribution. Select all that apply. Multiple select question. The probability of an outcome is between 0 and 1 inclusive. The sum of the probabilities of all possible outcome is one. The distribution is symmetrical. Reason: Not necessarily. Half of the possible outcomes have associated probabilities greater than 0.5 Reason: All of the probabilities could be less than 0.5. The outcomes are mutually exclusive events. • Experiment matches Choice, selecting and weighing the apples selecting and weighing the apples • outcome matches Choice, 165 grams average weight 165 grams average weight • event matches Choice, an average weight between 150 and 165 grams an average weight between 150 and 165 grams • random variable matches Choice, The average weight of five apples The average weight of five apples

A quantity representing the outcome of a random experiment that can assume different values is called a: Multiple choice question. probability Reason: A probability is associated with a particular value of a random variable. mutually exclusive event Reason: The outcomes of a random variable that make up a probability distribution are mutually exclusive. random variable probability distribution Reason: A probability distribution describes a random variable. Choose the random variables from this set that are discrete. Select all that apply. Multiple select question. The number of persons riding on a bus. The life span of a parakeet. Reason: Life span is measurement of time, which is continuous. The number of concert tickets sold. The height of a person from a class of eight. Reason: Although the people are discrete, their height is not. Which of the following statements is the best definition of a Continuous Random Variable? Multiple choice question. A random variable that can assume any value within a range of values. A random variable that can assume only certain separate values. Reason: This is a discrete variable A random variable that has an infinite number of values, such as the whole numbers. Reason: A variable can take on an infinite number of values, but still be discrete, if there is a clear separation between values. In a binomial experiment the variable is the number of successes in a fixed number of trials and the probability of success is the same for each trial. Which two of the following statements also describe features of a binomial experiment? Multiple select question. Trials are independent. The distribution is always symmetrical. Reason:

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It is only symmetrical if P(success)=50%. The trials represent selection without replacement. Reason: No. Independent trials imply replacement. The outcome of a trial can be classified as either a success or a failure. A random variable can be defined as: Multiple choice question. a quantity resulting from a random experiment that can have different values One from a set of variables representing different outcomes to a chance experiment Reason: One variable is used to represent all outcomes. a variable chosen by chance to represent the outcomes of an experiment Reason: It is the value, not the variable that is random. True or false: The standard deviation of a probability distribution is the square root of the variance of the probability distribution. True false question. True False Reason: The standard deviation is defined as the square root of the variance. Choose the two random variables from this list that are continuous. Multiple select question. The wait time at the dentist. The average temperature in NYC during May. The number of ads during a television show. Reason: This random variable can assume only certain clearly separated values.

The number of apples per bag in a supermarket. Reason: This random variable can assume only certain clearly separated values. The formula for the variance of a binomial distribution is σ 2 = nπ(1 - π). What do the symbols n and π represent in this formula? Multiple choice question. number of trials and P(success) number of trials and random variable Reason: number of trials and P(success) random variable and combination Reason: number of trials and P(success) combination and and P(success) Reason: number of trials and P(success) A Binomial experiment has independent trials and the outcome of a trial can be classified as either a success or a failure. Which two of the following statements also describe features of a binomial experiment? Multiple select question. After the first trial, subsequent trials are conditional probabilities. Reason: No. Independence implies that the trial probabilities are not changed by previous events. The random variable counts the number of successes in a fixed number of trials. The probability of success stays the same for each trial. The distribution is always asymmetric in shape. Reason: If P(success)=0.5 then the distribution is symmetrical. A binomial distribution has n = 10 trials with a probability of success of π=0.4. Calculate the mean of this binomial distribution,. Multiple choice question. 0.6 Reason: This is the probability of a failure. 0.4 Reason: This is the probability of a success. You must multiply this by the n. 4 5 Reason: Multiple n by π. 2.4

Reason: This is the variance. A binomial distribution has 8 trials and a probability of success of 0.2. Calculate the variance for this distribution. Multiple choice question. 1.60 Reason: This is the mean. 0.80 Reason: This is the probability of a failure. 1.28 1.13 Reason: This is the standard deviation. A software salesman knows that on average he will make one sale for every ten companies he calls. Let "success" be making a sale. (P(success)=0.10) Use binomial probability formula to find the chance that he will make two sales if he calls 6 companies. Multiple choice question. 0.250 Reason: x=2, n=6, π=0.1; P(2)= 6 C 2 (0.1) 2 (0.9) 4 0.033 Reason: x=2, n=6, π=0.1; P(2)= 6 C 2 (0.1) 2 (0.9) 4 0.333 Reason:

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x=2, n=6, π=0.1; P(2)= 6 C 2 (0.1) 2 (0.9) 4 0.098 The table provides binomial probabilities for n=6. If 80% of drivers admit to talking on their cell phone while they drive, what is the probability that half of 6 randomly sampled adults would indicate they talk on their cell phones while driving? Multiple choice question. 0.960 Reason: This is the variance. 0.015 Reason: Did you look up the wrong value of π? 0.082 4.800 Reason: A probability must be between 0 and 1, inclusive. This is the mean. The formula for the mean of a binomial distribution is μ = nπ. What do the symbols n and π represent in this formula? Multiple choice question. number of trials and random variable Reason: number of trials and P(success) number of trials and P(success) random variable and combination Reason: number of trials and P(success) combination and and P(success)

Reason: number of trials and P(success) When can a binomial distribution be used as a good approximation to a hypergeometric distribution? Multiple choice question. We are sampling, without replacement, from a small population, so the trials are dependent. Reason: This is when you should use a hypergeometric distribution. When the sample size is more that 5% of the population. Reason: Use a hypergeometric distribution in this case. When the sample size (n) is less than 5% of the population. Reason:

This will mean that the samples are almost independent. It is easier to use a binomial probability table instead of calculating the probability under what circumstances? Multiple choice question. When π is greater than one . Reason: π is a probability and can never be greater than one. When π is two or more digits. Reason: Many tables give π to only one decimal, so it may be necessary to calculate the probability to obtain better accuracy. When n is large. When n is small. Reason: Calculation is easier when n is small. Suppose a problem asks for the probability of more than two successes when there are only ten trials. Which one of these expressions would provide the answer? Select all that apply. Multiple select question. P(x=0)+P(x=1)+P(x=2) Reason: This will find the probably of two or less. P(x=3)+P(x=4)+...+P(x=9)+P(x=10) 1-P(x=0)-P(x=1)-P(x=2) Reason: This uses the Complement Rule to find the correct answer. P(x=0)+P(x=1) Reason: This will find the probability of less than two. P(x=2) Reason: This will find the probably of exactly two. Which of the following statements describes the relationship between the Poisson distribution and the binomial distribution? Multiple choice question. It is a limiting form of the binomial distribution when the probability of success (π) is very small and the sample (n) is very large. It is a form of the binomial distribution that occurs when the sample size (n) is very large, and the probability of success (π) is close to 0.5. Reason: This describes the normal approximation of the binomial distribution.

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It is a limiting form of the binomial distribution when the sample size (n) is a large part of the population (N). Reason: This describes the hypergeometric distribution. The formula used to calculate Hypergeometric probabilities is P(x) = (SCx)(N −SCn− x)NCn What does P(x) represent?. Multiple choice question. the number of successes in the population Reason: A list of the outcomes of a random experiment and the probability of each outcome. the number of successes in the sample Reason: A list of the outcomes of a random experiment and the probability of each outcome. probability of a specific x the number of trials Reason: A list of the outcomes of a random experiment and the probability of each outcome. Which of the following statements describe the Poisson Distribution? Select all that apply Multiple select question. The probability of an individual event occurring is quite large. Reason: The probability of "success" is small, and proportional to interval length. The probability of the event is proportional to the interval size. The intervals do not overlap and are independent. The random variable is the number of occurrences during an interval. Which of the following statements is true for both the binomial and Poisson distributions? Multiple choice question. A random variable that can assume any value within a range of values. Reason: This is a characteristic of a continuous distribution. Both are discrete probability distributions. the sample size (n) is very large, and the probability of success (π) is close to 0.5. Reason: This describes the normal approximation of the binomial distribution. Which of the following statements are not true of the Poisson Distribution? Multiple choice question. The variance of the Poisson distribution is equal to its mean Reason: The variance and mean are equal. The intervals overlap and are not independent.

Reason: The intervals do not overlap and are independent. The probability of the event is proportional to the interval size. Reason: This is a characteristic of the Poisson distribution When can a binomial distribution be used as a good approximation to a hypergeometric distribution? Multiple choice question. We are sampling, without replacement, from a small population, so the trials are dependent. Reason: This is when you should use a hypergeometric distribution. When the sample size is more that 5% of the population. Reason: Use a hypergeometric distribution in this case. When the sample size (n) is less than 5% of the population. Reason: This will mean that the samples are almost independent. A grocer checks 200 apples and finds that 8 are spoiled. On average, how many apples are spoiled in a bag of ten? (Hint: spoilage will follow a Poisson distribution, let n=10 and π is the empirical probability.) Multiple choice question. 2 Reason: μ=nπ 0.4 Reason: This mean can be used to calculate Poisson probabilities. 0.2 Reason: μ=nπ 0.04 Reason: π=8/200, now find μ Which of the following statements describe the Poisson Distribution? Select all that apply Multiple select question. The probability of an individual event occurring is quite large. Reason: The probability of "success" is small, and proportional to interval length. The intervals do not overlap and are independent. The probability of the event is proportional to the interval size. The random variable is the number of occurrences during an interval.

Under what circumstances should you use the hypergeometric distribution instead of the binomial distribution? Multiple choice question. When the population size, N, is much larger than the sample size, n, meaning that the trials give approximately the same probability. The random variable is the number of successes in a fixed number of trials. When the observations are mutually exclusive and collectively exhaustive. When can a binomial distribution be used as a good approximation to a hypergeometric distribution? Multiple choice question. We are sampling, without replacement, from a small population, so the trials are dependent. Reason: This is when you should use a hypergeometric distribution. When the sample size (n) is less than 5% of the population. Reason: This will mean that the samples are almost independent. When the sample size is more that 5% of the population. Reason: Use a hypergeometric distribution in this case.

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CHAPTER 8 Which of the following statements correctly describe the relationship between a population and a sample? Select all that apply. Multiple select question. A sample statistic is probably not exactly the same as the corresponding population characteristic Reason: This is called sampling error. Samples are used to estimate population characteristics. A sample is a subset of the population. A "population" is part of a sample. Reason: A sample is part of a population. Which of the following statements describe valid reasons to use a sample instead of evaluating a much larger population? Select all that apply. Multiple select question. A sample can be chosen to validate a specific idea about the population. Reason: True, but it would be a biased sample, and would be lying with statistics. Contacting the entire population would be time consuming. Sampling is a random process, and therefore more accurate than measuring the whole population. Reason: A valid sample must be random, but is always a little less accurate than evaluating the population. Contacting the whole population would be only marginally more accurate than a sample. Economics plays a role in the sampling process. Which statements correctly describe this relationship? Select all that apply. Multiple select question. The cost of studying an entire population may be prohibitive. Reason: You can't do what you can't afford. Larger samples cost more, and increasing size gives diminishing marginal returns in accuracy. Reason: You must balance needed accuracy and cost. Doubling sample size doubles accuracy and is worth the cost. Reason: As sample size increases, gains in accuracy are not justified. There are "economies of scale" in using a very large sample. Reason: The diminishing returns in accuracy may trump any such cost savings.

Other reasons besides cost and size may make it difficult or impossible to evaluate the entire population. Which of the following describe such reasons? Select all that apply. Multiple select question. The population may be changing too fast to allow complete sampling. Reason: For example, the human population. A large part of the population may be physically inaccessible. Reason: Some persons hide from census takers! The population may consist of differing sub-populations. Reason: This may be true, but still not prohibit evaluating the entire population. "Destructive Testing" destroys a sample in the course of measuring it. Which of the following are examples of this process? Select all that apply. Multiple select question. Weighing a cereal to be sure each box contains the advertised amount. Asking voters how they will cast their ballots in the next election. Reason: At least this isn't destructive in most countries! Evaluating coffee for taste and aroma. Determining a table's maximum load capacity by increasing its load until it breaks. Which of the following are true regarding parameters and statistics? Multiple choice question. μ is a parameter and s 2 is a statistic. Parameters are measures calculated from samples. Reason: Parameters are from populations. σ is a statistic and s is a parameter. Reason: σ is the symbol for the population standard deviation; thus, it is a parameter. s is the symbol for the sample standard deviation; thus, it is a statistic. Statistics are measures calculated from populations. Reason: Statistics are from samples. What is a simple random sample? Choose one. Multiple choice question. A random sample with fewer than 10 items included in the sample. Reason: "Simple" does not refer to size. A sample chosen so that the extreme observations are included. Reason:

Simple random samples do not ensure that any particular observations are included in the sample. A sample selected so that each member of the population has the same likelihood of being included. A sample chosen in the easiest way possible for the researcher so that data may be collected quickly. Reason: The easiest samples rarely give each member of the population the same chance of being selected. Taking a random sample can be a complex process. There are many reasons why it may be undesirable to sample an entire population. Which of the following is a reason that a modest size sample may be adequate? Multiple choice question. The population is highly varied, and a small sample may reflect only a part of it. Reason: This is a reason to take a larger sample. Very few problems require 100% accuracy. A large but biased sample may do more harm than a smaller unbiased sample. Reason: This is a reason for careful. random sampling, Not for choosing sample size. Which one of the following describes a random process that could be used to create a simple random sample? Multiple choice question. Asking your friends to choose a sample for you. Reason: Could you be sure they would use a random process? Selecting items from the population in a manner that is most convenient for the researcher. Reason: Convenient samples often result in bias. Assigning numbers to members of the population and drawing the numbers out of a hat. Reason: The list could be used in place of a random number table. Economics plays a role in the sampling process. Which statements correctly describe this relationship? Select all that apply. Multiple select question. Doubling sample size doubles accuracy and is worth the cost. Reason: As sample size increases, gains in accuracy are not justified. There are "economies of scale" in using a very large sample. Reason: The diminishing returns in accuracy may trump any such cost savings. Larger samples cost more, and increasing size gives diminishing marginal returns in accuracy.

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Reason: You must balance needed accuracy and cost. The cost of studying an entire population may be prohibitive. Reason: You can't do what you can't afford. Which of the following distinguish systematic random sampling from simple random sampling? Select all that apply. Multiple select question. Simple random sampling is more prone to bias. Reason: It is less prone to bias. Systematic random sampling is quicker and easier. Systematic random sampling uses only one random choice, instead of several. Reason: Simple random sampling uses a random event for each sample item. Simple random sampling requires fewer random numbers. Reason: It requires many more. Other reasons besides cost and size may make it difficult or impossible to evaluate the entire population. Which of the following describe such reasons? Select all that apply. Multiple select question. A large part of the population may be physically inaccessible. Reason: Some persons hide from census takers! The population may consist of differing sub-populations. Reason: This may be true, but still not prohibit evaluating the entire population. The population may be changing too fast to allow complete sampling. Reason: For example, the human population. Identify the steps required in taking a systematic random sample. Select all that apply. Multiple select question. Select the first k items from the population. Reason: This will introduce bias if the population has intrinsic order. Select a random starting point. Reason: By using a random process. Select every kth member of the population from the starting point. Select a random number k. Reason: k is not random, but depends on the sample size.

When is it inappropriate to use systematic random sampling? Multiple choice question. When the population is much larger than the sample size. Reason: A large population is a good reason to consider Systematic sampling. When there is no physical order to the population. Reason: This is when you can use it. When the order of items in the population is related to some particular characteristic. When time and resources for sampling and analysis are limited. Reason: This is a good reason to consider systematic sampling, because it is easier. What is a simple random sample? Choose one. Multiple choice question. A sample selected so that each member of the population has the same likelihood of being included. A random sample with fewer than 10 items included in the sample. Reason: "Simple" does not refer to size. A sample chosen so that the extreme observations are included. Reason: Simple random samples do not ensure that any particular observations are included in the sample. A sample chosen in the easiest way possible for the researcher so that data may be collected quickly. Reason: The easiest samples rarely give each member of the population the same chance of being selected. Taking a random sample can be a complex process. What characteristic of a population requires the use of stratified random sampling to avoid bias? Multiple choice question. The population has no order or subgroups related to the characteristic of interest. Reason: Lack of ordering of the data does not create strata. The population has an intrinsic order based on some characteristic. Reason: Ordering of the data, by itself, does not create strata. The population is clearly divided into groups based on some characteristic. How is a table of random numbers used to select a random sample? Choose the steps that make up the process.

Multiple select question. numbers are chosen systematically from the random number table Items from the population are assigned sequential numbers. items whose numbers correspond to random numbers become the sample numbers are always chosen by starting in the upper left corner Reason: This would always result in the same assigned numbers being selected. A marketing firm is polling 60 students at a college using a stratified sample. If two thirds of the students are women, and one quarter of the students are from out of state, how many out-of-state students should be polled? Multiple choice question. 15 Reason: One quarter of the sample. 40 Reason: This is how many women should be polled. 45 Reason: This would be the correct number for in-state students. 20 Reason: This would be the correct number for male students. =60*1/4 Why is systematic random sampling sometimes used in place of simple random sampling? Multiple choice question. It is more time consuming, but less prone to bias. Reason: It is more prone to bias. It gives a more random sample. Reason: Actually it may be less random. Sometimes it is difficult to assign random numbers. It makes use of a greater number of random choices. Reason: It only uses one. Simple random sampling uses one for each sampled item. Which of the following populations is a good candidate for Systematic random sampling? Multiple choice question. Students at a high school, arranged in order of their birth date. Reason: Chronological order can introduce bias. Companies listed on the New York Stock Exchange. Reason:

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There is no obvious intrinsic order in this population. The Fortune 500 list of corporations. Reason: These are ordered by economic rank, a serious source of bias. A customer list ordered by sales volume. Reason: This ordered list may result in a biased sample. If a researcher was studying semester loads of students, which of the following might represent strata that would be appropriate for stratified random sampling? Select all that apply. Multiple select question. Grouping students by marital status. Reason: Married students may have different loads than unmarried students. Grouping students by last name. Reason: Semester load would have no relationship with last name. Grouping students by hair color. Reason: Semester load would have no relationship with hair color. Grouping students as employed and unemployed. Reason: Employed students may different loads than unemployed students. Which of the populations listed below is a natural candidate for cluster sampling? Multiple choice question. The employees of a farm equipment manufacturer, who are both men and women Reason: Stratified sampling is appropriate. The voters in a state, who are grouped into political districts. Reason: The clusters are already defined! The wage earners in a large city, who have varied salaries. Reason: Stratified or Simple sampling is appropriate. Identify the steps that are followed in taking a stratified random sample. Select all that apply. Multiple select question. Take a sample of size n/k from each strata, where n is sample size and k is the number of strata. Reason: No. The size of sample from each strata is proportional to its fraction of the population size. Take random samples from each strata.

Take a systematic sample from the population as a whole. Reason: This has no role in stratified sampling. Measure the size of the strata as a proportion of the population. Determine what portion of the sample should come from each strata. Identify the steps involved in taking a cluster sample. Select all that apply. Multiple select question. Select a random sample from each sub group. Arrange the clusters into logical order, reflecting the desired characteristic. Reason: Ordering of clusters in not normally part of the process. Eliminate any clusters that are too difficult to sample. Reason: No systematic choice of clusters is appropriate! It must be random. Divide the population into groups using naturally occurring boundaries. Reason: Such as geographical, political or demographic boundaries. Randomly select a subset of clusters. Which of the following distinguish systematic random sampling from simple random sampling? Select all that apply. Multiple select question. Systematic random sampling uses only one random choice, instead of several. Reason: Simple random sampling uses a random event for each sample item. Simple random sampling is more prone to bias. Reason: It is less prone to bias. Systematic random sampling is quicker and easier. Simple random sampling requires fewer random numbers. Reason: It requires many more. Choose the statement that best defines the Sampling Distribution of the Sample Mean. Multiple choice question. A distribution showing the variation in sample means resulting from different sample sizes. Reason: No. It refers to samples of the same size. A probability distribution of all possible sample means of a given sample size. A probability distribution showing the mean and standard deviation of the population. Reason: No. It shows the distribution of the samples means.

Identify the steps required in taking a systematic random sample. Select all that apply. Multiple select question. Select a random number k. Reason: k is not random, but depends on the sample size. Select the first k items from the population. Reason: This will introduce bias if the population has intrinsic order. Select a random starting point. Reason: By using a random process. Select every kth member of the population from the starting point. The Central Limit Theorem describes an expected distribution shape. Which of these statements is correct? Multiple choice question. If the population is skewed, left or right, the sampling distribution of the sample mean will be uniform. The sampling distribution of the sample mean is nearly normal. As the sample size decreases, the sampling distribution of the sample mean more closely approaches the normal distribution. What characteristic of a population makes it a good candidate for cluster sampling? Multiple choice question. The population is naturally arranged into one cluster in a small area. Reason: Cluster sampling is used when data is spread over a large area. The population has an intrinsic order that is related to its characteristics. Reason: This kind of population requires systematic sampling. The population has identifiable sub groups. Reason: This kind of population requires stratified sampling. The population is widely scattered over a large geographical area. Reason: This makes it difficult and expensive to do a simple random sample. In cluster sampling the clusters are chosen from the population using simple random sampling. What kind of sampling is used within the individual clusters? Multiple choice question. Judgment sampling Reason: Judgment sampling creates bias. Convenience sampling Reason:

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Convenience sampling creates bias. Non-probability sampling. Reason: Non-probability sampling creates bias. Random sampling Reason: When sampling is used, it is done randomly. Sometimes a census is taken of selected clusters. Which of the following is an expression that represents sampling error? Multiple choice question. X - μ μ - σ Reason: This is the difference in two population parameters. X -s Reason: This is the difference in two sample statistics. s-s 2 Reason: This is the difference in two sample statistics. Choose the two statements that are correct descriptions of the sampling distribution of the sample mean. Multiple select question. It is a probability distribution of all possible sample means. It is a probability distribution of population parameters corresponding to a given sample statistic. Reason: It shows a distribution of sample statistics. It is a distribution of means from samples of all sizes. Reason: No. Only one size. It is a distribution of means from samples of all one size. Pick the statement that describes the formula for the standard error of the mean in ordinary language. Multiple choice question. The standard error is equal to the sample standard deviation divided by the square root of the sample size. The standard error is equal to the population standard deviation divided by the square root of the sample size. The standard error of the sample means equals the population standard deviation multiplied by the square of the sample size.

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Which of the following statements correctly describe characteristics of the set of sample means? Select all that apply. Multiple select question. The standard deviation of the sample means is the same as the population standard deviation. Reason: They are different things. One measures the dispersion of sample means, the other the dispersion of population measures. The dispersion of the sample means is narrower than the population dispersion. The distribution of sample means is nearly normal if the sample size is large. The mean of the samples is less than the mean of the population. The mean of the sample means equals the mean of the population. There are two conditions under which we can assume that the sample means follow a normal distribution. What are they? Multiple select question. We know that the population is uniformly distributed. Reason: If this is true, we would have to use a large sample size. Our sample is small, but we know the population distribution is highly skewed. Reason: In this case, we would expect that the sample mean distribution is not normal. We don't know the population distribution, but the sample size is 30 or larger. We know that the population is normally distributed. Which statement correctly describes the relationship between the mean of the sample means and the population mean? Multiple choice question. The mean of the sample means is smaller than the population mean. Reason: The sample means center around the same value the population centers around - μ. The mean of the sample means is equal to the population mean divided by the square root of the sample size. Reason: The sample means center around the same value the population centers around - μ. The mean of the sample means is the same as the population mean if the population distribution is normal. Reason: The Central Limit Theorem says that the sample mean is independent of the population distribution for large samples. The mean of the sample means equals the population mean. Reason: μ x = μ Choose the statement that best describes sampling error. Multiple choice question.

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The difference between a sample statistic and its corresponding population parameter. A sample statistic that is not correctly calculated. Reason: This is an error, but not what is meant by sampling error. A sample that is selected using a process that is not random. Reason: While this may involve bias, it is not what we mean by "sampling error". Which one of the following statements is true about the dispersion of the distribution of sample means? Multiple choice question. As the sample size increases, the variability in the sample means increases. Reason: Larger sample sizes make the sample means more alike. As the sample size increases, the variability in the sample means approaches the population mean. Reason: The variability in the sample means is not related to the population mean. As the sample size increases, the variability in the sample means approaches the population standard deviation. Reason: The variability in the sample means is always smaller than the variability in the population. As the sample size increases, the variability in the sample means decreases. The average height of American women (in 2016) is 5 ft. 4 inches (64 inches) with a standard deviation of 3 inches. What is the probability that the average height of a random group of nine American women would be less than five feet three inches? Assume that the heights of American women are normally distributed. Multiple choice question. -1.00 Reason: Probabilities can't be negative. This is the z-value. 0.3413 Reason: You need the area below 63 inches. 0.8413 Reason: You found the area above 63 inches. 0.1587 Reason: z= (63−64) ( 39 √ ) =−1 The probability corresponding to z- value of −1 is 0.1587.

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There are two conditions under which we can assume that the sample means follow a normal distribution. What are they? Multiple select question. We know that the population is normally distributed. We don't know the population distribution, but the sample size is 30 or larger. We know that the population is uniformly distributed. Reason: If this is true, we would have to use a large sample size. Our sample is small, but we know the population distribution is highly skewed. Reason: In this case, we would expect that the sample mean distribution is not normal. The Central Limit Theorem describes an expected distribution shape. Which of these statements is correct? Multiple choice question. As the sample size decreases, the sampling distribution of the sample mean more closely approaches the normal distribution. Reason: Larger samples sizes more closely approach the normal distribution. The sampling distribution of the sample mean is nearly normal. If the population is skewed, left or right, the sampling distribution of the sample mean will be uniform. Reason: No. The Central Limit Theorem says the sampling distribution will approach the normal distribution. Select the formula that would be used to find the z-value for a sample mean when we are applying the Central Limit Theorem. Which of the following is an expression that represents sampling error? Multiple choice question. X - μ

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The average height of American males (in 2016) is 5 ft. 9 1/2 inches (69.5 inches) with a standard deviation of 3 inches. What is the probability that the average height of a random group of 16 American men would be over five feet ten inches? Assume that the heights of American men are normally distributed.

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chapter 8

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