Chapter 7

Question 1

What is the term for a group of objects or people to be studied?

a. Sample
b. Estimator
c. Census
d. Population

Answer 1

d. Population

Question 2

What is the numerical value that characterizes some aspect of a population?

a. Statistic
b. Parameter
c. Estimator
d. Census

Answer 2

b. Parameter

Question 3

What is an important difference between statistics and parameters?

a. Statistics are knowable, but parameters are typically unknown
b. Parameters are easier to measure than statistics
c. Parameters are knowable, but statistics are typically unknown
d. Statistics are more reliable than parameters

Answer 3

a. Statistics are knowable, but parameters are typically unknown

Question 4

To keep track of parameters and statistics, parameters are represented by Greek characters while statistics are represented by which of the following?

a. Roman numerals
b. Polygons
c. Binary numbers
d. English letters

Answer 4

d. English letters

Question 5

When is a method called “biased”

a. It has a tendency to produce an untrue value
b. It always produces an untrue value
c. It is difficult to use
d. It is complicated to carry out

Answer 5

a. It has a tendency to produce an untrue value

Question 6

A researcher has designed a survey in which the questions asked do not produce a true answer. What is this an example of?

a. Sampling bias
b. Nonresponse bias
c. Voluntary response bias
d. Measurement bias

Answer 6

d. Measurement bias

Question 7

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

Answer 7

d. Both A and B

Question 8

Explain the difference between a parameter and a statistic

a. A statistic is a measure of the population, and a parameter is the measure of a sample
b. A parameter is the measure of the population, and a statistic is a measure of the sample
c. A parameter is a categorical measure of a population, and a statistic is a numerical measure of a population

Answer 8

b. A parameter is a measure of the population and a statistic is a measure of a sample

Question 9

Two symbols are used for the mean: mu and x overbar.

a. Which represents a parameter and which a statistic?
b. In determining the mean age of all students at your school, you survey 30 students and find the mean of their ages. Is this mean mu or x overbar?

Answer 9

The symbol (mu) represents a parameter and x over bar represents a statistic

The mean is x over bar

Question 10

The mean GPA of all 3000 students at a college is 3.12. A sample of 100 GPAs from this school has a mean of 2.58. Which number is (mu) and which is (x-over-bar)?

a. The statistic 3.12 is mu and the parameter is x-over-bar = 2.58
b. The population mean is mu = 3.12 and the sample mean is x-over-bar = 2.58

Answer 10

b. The population mean is mu = 3.12 and the sample mean is 2.58

Question 11

The mean GPA of all 3000 students at a college is 3.12. A sample of 100 GPAs from this school has a mean of 2.58. Which number is mu and which is x overbar​?

Answer 11

The population mean is mu equals 3.12​, and the sample mean is x over bar equals 2.58.

Question 12

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?

Answer 12

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

Question 13

Suppose you find all the heights of the members of the​ men’s basketball team at your school. Could you use those data to make inferences about heights of all men at your​ school? Why or why​ not?

A. One could use these data to make inferences about heights of all men at the school because the sample includes all members of the basketball team.

B. One should not use these data to make inferences about heights of all men at the school because the data suffer from measurement bias.

C. One could use these data to make inferences about heights of all men at the school because the sample is unbiased and representative of the population.

D. One should not use these data to make inferences about heights of all men at the school because the sample is not random and is not representative of the population.

Answer 13

D. One should not use these data to make inferences about heights of all men at the school because the sample is not random and is not representative of the population

Question 14

T/F A measurement process is biased if it systematically overstates or understates the true value of the measurement.

Answer 14

True

Question 15

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.

Answer 15

If you test all the batteries to failure, you will have no batteries to sell

Question 16

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.Explain sampling with replacement

Answer 16

Draw a notecard, note the name, replace the notecard and draw again. It is possible that the same student could be picked twice

Question 17

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.Explain sampling without replacement

Answer 17

Draw a notecard, note the name and do not replace the notecard and draw again. it is not possible that the same student could be picked twice

Question 18

Tyler is interested in whether Proposition P will be passed in the next election. He goes to the university library and takes a poll of 100 students. Since 55​% favor Proposition​ P, Tyler believes it will pass. Explain what is wrong with his approach.

Answer 18

a. Tyler took a convenience sample. The students may not be representative of the voting population, so the proposition may not pass

Question 19

A teacher at a community college sent out questionnaires to evaluate how well the administrators were doing their jobs. All teachers received​ questionnaires, but only​ 10% returned them. Most of the returned questionnaires contained negative comments about the administrators. Explain how an administrator could dismiss the negative findings of the report.

a. This was only one survey and people’s opinions change over time.
b. There is measurement bias. The questions could have been worded in such a way that the respondents responses were influenced.
c. The entire population was surveyed and therefore inferences cannot be drawn.
d. There is nonresponse bias. The results could be biased because the small percentage who chose to return the survey might be very different from the majority who did not return the survey.

Answer 19

D. There is nonresponse bias. The results could be biased because the small percentage who chose to return the survey might be very different from the majority who did not return the survey.

Question 20

A phone survey asked whether Social Security should be continued or abandoned immediately. Only landlines​ (not cell​ phones) were called. Do you think this would introduce​ bias? Explain.

Answer 20

B. This would likely introduce sampling bias because older people would be more likely to be surveyed than younger people, and older people are less likely to favor abandoning Social Security

Question 21

If you walked around your school campus and asked people you met how many keys they were​ carrying, would you be obtaining a random​ sample? Explain.

a. Yes, you would be obtaining a random sample
b. As long as you surveyed at least 100 people, you would be obtaining a simple random sample
c. No, you would be obtaining a convenience sample and not a random sample
d. No, you would be obtaining a biased sample

Answer 21

d. No, you would be obtaining a biased sample

Question 22

To measure the quality of a survey, statisticians evaluate which of the following?

a. Outcome of the survey
b. Population being measured
c. Method used for the survey
d. all of the above

Answer 22

c. The method used for the survey

Question 23

When taking samples from a population and computing the proportion of each sample, which of the following values is always the same?

a. The sample proportion
b. The population proportion
c. The accuracy of each sample proportion in estimating the population proportion
d. All of the above

Answer 23

b. The population proportion

Question 24

What is the standard deviation of the sampling distribution called?

Answer 24

a. Sampling error
b. Bias
c. Standard error
d. Precision

Question 25

How is the bias of a sampling distribution measured? a. By looking at the size of the samples in the sampling distribution b. Using the standard error of the sampling distribution c. By computing the distance between the center of the sampling distribution and the population parameter

Answer 25

c. By computing the distance between the center of the sampling distribution and the population parameter

Question 26

T/F the precision of an estimator does not depend on the size of the population

Answer 26

True

Question 27

T/F The precision of an estimator does not depend on the size of the sample

Answer 27

False

Question 28

T/F Surveys based on larger sample sizes have larger standard errors

Answer 28

False

Question 29

Know the difference between bias and precision

Answer 29

Bias is a measure of accuracy and precision is a measure of consistency

Question 30

Suppose​ that, when taking a random sample of 8 from 183 ​women, you get a mean height of only 60 inches​ (5 feet). The procedure may have been biased. What else could have caused this small​ mean? a. Nothing other than bias could have caused this small mean b. The device used for measuring may be set up incorrectly to give all the heights as less than they are c. The small mean might have occurred by chance d. The measurements may not have been precise

Answer 30

c. The small mean might have occurred by chance

Question 31

T/F the error is the difference between p-hat and p (p-hat - p)

Answer 31

True

Question 32

Which of the following conditions regarding sample size must be met to apply the Central Limit Theorem for sample proportions? a. The sample size is large enough that the sample expects at least 10 successes and 10 failures b. The sample size must be 1/10 the population size c. The sample size must be at least 1/2 the population size

Answer 32

a. The sample size is large enough that the sample expects at least 10 successes and 10 failures

Question 33

If the sample is collected without​ replacement, which conditions regarding the population must be met to apply the Central Limit Theorem for Sample​ Proportions?

Answer 33

The population size must be at least 10x bigger than the sample size

Question 34

When applying the Central Limit Theorem for Sample​ Proportions, which of the following can be substituted for p when calculating the standard error if the value of p is​ unknown? a. The value of the sample standard deviation b. the value of the sample mean c. The value of the sample proportion d. None of these.

Answer 34

c. The value of the sample proportion

Question 35

To check the condition that the sample size is large enough before applying the Central Limit Theorem for Sample​ Proportions, researchers can verify that the products of the sample size times the sample proportion and the sample size times ​(1minussample ​proportion) are both greater than or equal to what​ number?

Answer 35

10

Question 36

If the conditions of a survey sample satisfy those required by the Central Limit​ Theorem, then there is a​ 95% probability that a sample proportion will fall within how many standard errors of the population​ proportion? a. 1.5 b. 2 c. 1 d. 3

Answer 36

b. 2 standard errors

Question 37

According to a candy​ company, packages of a certain candy contain 15​% orange candies. Find the approximate probability that the random sample of 500 candies will contain 17​% or more orange candies. a. Find the mean (p-hat = p) b. Find the standard deviation

Answer 37

a. mean = .15 b. SE: .016 A: .106 (7.3.35 6/10)

Question 38

Juries should have the same racial distribution as the surrounding communities. About 25​% of residents in a certain region are a specific race. Suppose a local court randomly selects 250 adult citizens of the region to participate in the jury pool. Use the Central Limit Theorem​ (and the Empirical​ Rule) to find the approximate probability that the proportion of available jurors of the above specific race is more than two standard errors from the population value of 0.25. The conditions for using the Central Limit Theorem are satisfied because the sample is​ random; the population is more than 10 times 250​; n times p is 63​, and n times​ (1 minus​ p) is 188​, and both are more than 10.

Answer 38

Because the sampling distribution for the sample proportion is approximately normal, it is known that the probability of falling within two standard errors is about 0.95. Therefore, the probability of falling more than 2 standard errors away from the mean is about 0.05

Question 39

According to a regional Bar​ Association, approximately 60​% of the people who take the bar exam to practice law in the region pass the exam. Find the approximate probability that at least 64​% of 200 randomly sampled people taking the bar exam will pass. Answer the questions below. a. The sample proportion is 0.64. What is the population proportion? b. The expected number of people that pass _______ is greater than _______ and the expected number of people who fail _____ is greater than 10. c. Find the standard error: d. Standardize Find the approximate probability that at least 0.64 pass by finding the area to the right of the z-value in the Normal curve The probability is represented but he area to the right of ____ because the question asks for the probability that the sample proportion will be at least _____ which translates to a z-score of 1.15. This means the question is asking for the probability that the z-score will be 1.15 or greater. Find the area of the shaded region in the figure to determine the probability.

Answer 39

a. 0.60 b. 120, 10, 80, 10 c. SE: 0.35 d.

Question 40

A recent study reported that 55​% of the children in a particular community were overweight or obese. Suppose a random sample of 500 public school children is taken from this community. Assume the sample was taken in such a way that the conditions for using the Central Limit Theorem are met. We are interested in finding the probability that the proportion of​ overweight/obese children in the sample will be greater than 0.52. Complete parts​ (a) and​ (b) below. a. Before doing any​ calculations, determine whether this probability is greater than​ 50% or less than​ 50%. Why?

Answer 40

a. This probability should be greater than 50% because 0.52 is less than the population proportion of 0.55 and because the sampling distribution is approximately Normal. b. Calculate the probability that 52​% or more of the sample are overweight or obese.

Question 41

A positive​ z-score occurs when the sample proportion is greater than the population proportion.

Answer 41

True

Question 42

A recent study reported that 55​% of the children in a particular community were overweight or obese. Suppose a random sample of 500 public school children is taken from this community. Assume the sample was taken in such a way that the conditions for using the Central Limit Theorem are met. We are interested in finding the probability that the proportion of​ overweight/obese children in the sample will be greater than 0.52. Complete parts​ (a) and​ (b) below.

Answer 42

Go to STAT Crunch -> Calculator -> Normal

Question 43

In a confidence interval, what information does the margin of error provide? a. How far the estimate is from the population value b. the amount of bias in our estimate c. the probability the estimate accurately measures the population value d. whether or not the conditions for the central limit theorem have been met

Answer 43

a. how far the estimate is from the population value

Question 44

Which of the following does the confidence level measure? a. The level of confidence the researchers have in their survey method b. The precision of the estimator c. The success rate of an individual interval in estimating the population proportion d. The success rate of the method of finding confidence intervals

Answer 44

d. The success rate of the method of finding confidence intervals

Question 45

What should be done to create a confidence interval for a population proportion? a. Add the margin of error to the sample proportion b. Subtract the margin of error from the sample proportion c. Add and subtract the margin of error to/from the sample proportion d. Multiply the margin of error and sample proportion

Answer 45

c. Add and subtract the margin of error to/from the sample proportion

Question 46

A random sample of likely voters showed that 65​% planned to vote for Candidate​ X, with a margin of error of 2 percentage points and with​ 95% confidence. Use a carefully worded sentence to report the​ 95% confidence interval for the percentage of voters who plan to vote for Candidate X.

Answer 46

"I am 95% confident that the population percentage of voters supporting Candidate X is between 63% and 67%"

Question 47

According to Q 46, is there evidence that Candidate X could lose?

Answer 47

"There is no evidence that the candidate could lose" The reason there is evidence is because the interval is entirely above 50%