MATH 221 - CH06

Suppose you knew the age at inauguration of all the past U.S. presidents. Could you use those data to make inferences about ages of past​ presidents? Why or why​ not? A. You can make inferences because the sample is not a random sample of the population. B. The sample size is not large enough to make inferences from. C. If you know all the ages at​ inauguration, you should not make inferences because you have the​ population, not a sample from the population.

C. note: You have the data for the entire population. It is not​ possible, and there is no​ reason, to make inferences because the population parameters are known.

Explain the difference between a parameter and a statistic. A. A parameter is a categorical measure of a​ population, and a statistic is a numerical measure of a population. B. A statistic is a measure of the​ population, and a parameter is a measure of a sample. C. A parameter is a measure of the​ population, and a statistic is a measure of a sample.

C. A parameter is a measure of the​ population, and a statistic is a measure of a sample. note: A parameter is a measure of the​ population, such as the average height of everyone in a​ school, and a statistic is a measure of a​ sample, such as the average height of 5 people randomly selected in the same school.

When is a method called​ "biased"? A.It always produces an untrue value. B.It is difficult to use. C.It has a tendency to produce an untrue value. D.It is complicated to carry out.

C.It has a tendency to produce an untrue value. note: A biased method will tend to produce an untrue​ value, though not in every case.

When reading about a​ survey, which of the following is important to​ know? A. What percentage of people who were asked to participate actually did so B. Whether the researchers chose people to participate in the survey or people themselves chose to participate C. How many questions were in the survey D. Both A and B E. ​A, B and C

D. Both A and B note: It is important to know whether there is nonreponse​ bias, which can be judged based on what percentage of people who were asked to participate actually did​ so, or voluntary response​ bias, which can be judged by whether the researchers chose people to participate in the survey or people themselves chose to participate.​ Therefore, it is important to know both A and B.

What is true of the shape of a binomial​ distribution? A. The shape depends solely on the probability of​ success, p. B. The shape depends solely on the number of​ trials, n. C. The shape never changes. D. The shape depends on both the number of​ trials, n, and the probability of​ success, p

D. The shape depends on both the number of​ trials, n, and the probability of​ success, p

To keep track of parameters and​ statistics, parameters are represented by Greek characters while statistics are represented by which of the​ following? Binary numerals English letters Polygons Roman numerals

English letters

What is a numerical value that characterizes some aspect of a​ population? Census Estimator Parameter Statistic

Parameter

What is the term for a group of objects or people to be​ studied? Population Census Sample Estimator

Population

Which of the following is not a characteristic that must be present in a binomial​ model? A. There is a fixed number of trials. B. There are only two outcomes for each trial. C. The probability of success is the same at each trial. D. The trials are dependent.

The trials in a binomial model are required to be independent.

What determines the exact shape of a Normal​ distribution? The values of the mean and the standard deviation The value of the mean The value of the mean and median The value of the standard deviation

The values of the mean and the standard deviation

What are statistics sometimes​ called? Parameters Populations Estimators Samples

A statistic is sometimes called an estimator. A statistic is a numerical characteristic of a sample

You are receiving a large shipment of batteries and want to test their lifetimes. Explain why you would want to test a sample of batteries rather than the entire population. A. If you test all the batteries to failure you would have no batteries to sell. B. The percentage of defective batteries can change in the time it takes you to test all the batteries. C. If you test all the batteries you cannot form any conclusions about the population.

A. note: If you test all the batteries to​ failure, you will not be able to sell any of them since none of them will work.

A researcher has designed a survey in which the questions asked do not produce a true answer. What is this an example​ of? Nonresponse bias Voluntary response bias Measurement bias Sampling bias

note: Measurement bias occurs when the method of data collection does not produce valid results.

The Normal model is a good​ first-choice to model data if the data are suspected to be​ _____.

symmetric and unimodal

The normal distribution is symmetric and​ _____.

unimodal

The binomial probability model is useful in many situations with variables of what​ kind? ​Discrete-valued numerical variables Categorical variables ​Continuous-valued numerical variables Both​ discrete-valued and​ continuous-valued variables

​Discrete-valued numerical variables note: The binomial probability model is useful in many situations with​ discrete-valued numerical variables because the outcome is often a count and only two outcomes are possible.

Explain the difference between sampling with replacement and sampling without replacement. Suppose you had the names of 10​ students, each written on a 3 by 5​ notecard, and want to select two names. Describe both procedures. Describe sampling with replacement. A. Draw a​ notecard, note the​ name, replace the notecard and draw again. It is possible the same student could be picked twice. B. Draw a​ notecard, note the​ name, do not replace the notecard and draw again. It is not possible the same student could be picked twice. C. Draw a​ notecard, note the​ name, do not replace the notecard and draw again. It is possible the same student could be picked twice. D. Draw a​ notecard, note the​ name, replace the notecard and draw again. It is not possible the same student could be picked twice.

A note: You draw one notecard and record the name. Because the sampling is done with replacement you put the notecard back. This means it is possible to draw the name again.

What are the values of the mean and the standard deviation for the standard Normal​ model? A. The standard normal model has a mean of 0 and a standard deviation of 1. B. The standard normal model has a mean of 1 and a standard deviation of 0. C. The standard normal model has a mean of 0 and standard deviation of 0. D. The standard normal model has a mean of 1 and a standard deviation of 1.

A. The standard normal model has a mean of 0 and a standard deviation of 1.

What is an important difference between statistics and​ parameters? A.Statistics are more reliable than parameters. B.Statistics are​ knowable, but parameters are typically unknown. C.Parameters are easier to measure than statistics. D.Parameters are​ knowable, but statistics are typically unknown.

B.Statistics are​ knowable, but parameters are typically unknown. note: A statistic is a measurable estimator of an often unknown population parameter.

What is the most widely used probability model for continuous numerical​ variables? The Normal distribution The probability density function The unimodal distribution The Central Limit Theorem

The Normal distribution

What is another name for the expected value of a probability​ distribution? The standard deviation The mean The variability of the distribution The shape of the distribution

The expected value of a probability distribution is another name for the mean of the distribution.