Question 1

A 95% confidence interval estimate of the population mean μ can be interpreted to mean that:

Accepted Answer

A)  if we repeatedly draw samples of the same size from the same population, 95% of the values of the sample means   will result in a confidence interval that includes the population mean μ. 
B)  there is a 95% probability that the population mean μ will lie between the lower interval limit and the upper interval limit. 
C)  we are 95% confident that we have selected a sample whose range of values does not contain the population mean μ. 
D)  we are 95% confident that 5% of the values of the sample means   will result in a confidence interval that includes the population mean μ. 
A)  if we repeatedly draw samples of the same size from the same population, 95% of the values of the sample means   will result in a confidence interval that includes the population mean μ. 
B)  there is a 95% probability that the population mean μ will lie between the lower interval limit and the upper interval limit. 
C)  we are 95% confident that we have selected a sample whose range of values does not contain the population mean μ. 
D)  we are 95% confident that 5% of the values of the sample means   will result in a confidence interval that includes the population mean μ. A

Question 2

Whenever a sampled population is normally distributed or whenever the conditions of the Central Limit Theorem are fulfilled, the sample mean   :

Accepted Answer

A)  is a consistent estimator of the population mean μ because the mean of the sampling distribution of the sample mean equals μ. 
B)  is an efficient estimator of the population mean μ because the mean of the sampling distribution of the sample mean equals μ. 
C)  is an unbiased estimator of the population mean μ because the mean of the sampling distribution of the sample mean equals μ. 
D)  is a biased estimator of the population mean μ because the mean of the sampling distribution of the sample proportion equals p. 
A)  is a consistent estimator of the population mean μ because the mean of the sampling distribution of the sample mean equals μ. 
B)  is an efficient estimator of the population mean μ because the mean of the sampling distribution of the sample mean equals μ. 
C)  is an unbiased estimator of the population mean μ because the mean of the sampling distribution of the sample mean equals μ. 
D)  is a biased estimator of the population mean μ because the mean of the sampling distribution of the sample proportion equals p. C

Question 3

Which of the following statements about the error bound B (also called the margin of error) is false?

Accepted Answer

A)  Statisticians routinely construct interval estimates by making their point estimate be the interval center and creating a range of other possible values, known as the error bound, below and above the center. 
B)  The error bound is a half-width of an interval estimate, equal to the difference between the point estimate on the one hand and either the lower or upper limit of the interval on the other hand. 
C)  The unknown parameter is presumed to lie at the center of the interval that the point estimate and the error bound create. 
D)  The error bound takes only sampling error into account, ignoring all other potential sources of error, such as bias in questions, selection bias, or miscalculations. 
A)  Statisticians routinely construct interval estimates by making their point estimate be the interval center and creating a range of other possible values, known as the error bound, below and above the center. 
B)  The error bound is a half-width of an interval estimate, equal to the difference between the point estimate on the one hand and either the lower or upper limit of the interval on the other hand. 
C)  The unknown parameter is presumed to lie at the center of the interval that the point estimate and the error bound create. 
D)  The error bound takes only sampling error into account, ignoring all other potential sources of error, such as bias in questions, selection bias, or miscalculations. C

Question 4

Which of the following statements is correct?

Accepted Answer

A)  A point estimate is an estimate of the range of a population parameter. 
B)  An interval estimate is an estimate of the range for a sample statistic. 
C)  A point estimate is a single-value estimate of the value of a population parameter. 
D)  A point estimate is an estimate of the midpoint of the range for a sample statistic. 
A)  A point estimate is an estimate of the range of a population parameter. 
B)  An interval estimate is an estimate of the range for a sample statistic. 
C)  A point estimate is a single-value estimate of the value of a population parameter. 
D)  A point estimate is an estimate of the midpoint of the range for a sample statistic.

Question 5

A local library is evaluating the possibility of expanding its hours of operation.The library staff want to estimate the mean number of persons who patronize the library during the peak weekday hours from 3:30 P.M.to 5:00 P.M.They randomly sample 12 weekdays and find an average attendance of 220.15, with a standard deviation of 22.4.What is a 90% confidence interval for the true mean weekly patronage during the peak hours?

Accepted Answer

A)  (208.627, 231.673) 
B)  (209.514, 230.787) 
C)  (179.920, 260.380) 
D)  (208.537, 231.763) 
A)  (208.627, 231.673) 
B)  (209.514, 230.787) 
C)  (179.920, 260.380) 
D)  (208.537, 231.763)

Question 6

For any arbitrary parameter   , a biased estimator of   is any estimate where:

Accepted Answer

A)  the expected value of the estimate equals   
B)  the expected value of the estimate differs from   
C)  the expected value of the estimate is greater than   
D)  the expected value of the estimate is less than   . 
A)  the expected value of the estimate equals   
B)  the expected value of the estimate differs from   
C)  the expected value of the estimate is greater than   
D)  the expected value of the estimate is less than   .

Question 7

Which of the following statements is false?

Accepted Answer

A)  The width of a confidence interval of the population mean narrows when the sample size increases. 
B)  The width of a confidence interval of the population mean narrows when the value of the sample mean increases. 
C)  The width of a confidence interval of the population mean widens when the confidence level increases. 
D)  The width of a confidence interval of the population mean is affected by the choice of confidence level. 
A)  The width of a confidence interval of the population mean narrows when the sample size increases. 
B)  The width of a confidence interval of the population mean narrows when the value of the sample mean increases. 
C)  The width of a confidence interval of the population mean widens when the confidence level increases. 
D)  The width of a confidence interval of the population mean is affected by the choice of confidence level.

Question 8

Faculty members at a local university complain that achieving tenure at their university takes much longer than at comparable universities.They randomly sample nine tenured faculty members at their university and find that the average time of service prior to tenure was 13.55 years, with a standard deviation of 1.98 years.What is a 95% confidence interval for the mean number of years of service to achieve tenure at this university?

Accepted Answer

A)  (12.028, 15.072) 
B)  (12.057, 15.043) 
C)  (12.256, 14.844) 
D)  (8.984, 18.116) 
A)  (12.028, 15.072) 
B)  (12.057, 15.043) 
C)  (12.256, 14.844) 
D)  (8.984, 18.116)

Question 9

Previous research indicates that 20% of homeowners do not carry sufficient homeowners' insurance to adequately protect their investment.We wish to estimate the percentage of homeowners in a particular suburban area who do not have adequate insurance.How many homes should we sample if we desire a 95% confidence interval with a width of no more than 6%?

Accepted Answer

A)  171 
B)  1068 
C)  267 
D)  683 
A)  171 
B)  1068 
C)  267 
D)  683

Question 10

In general, unbiased estimators are preferred for inference because:

Accepted Answer

A)  bias in inference is always bad and should be avoided at all costs, so using unbiased estimators is the only way to conduct objective inference. 
B)  unbiased estimators always have the least amount of variance of all possible estimators. 
C)  a biased estimator will almost always give very little insight into the parameter being estimated and, therefore, serves as a poor guess of the parameter's true value. 
D)  in many cases the most probable value of an unbiased estimator is the value of the parameter being estimated; thus, unbiased estimators typically converge on values near the parameter. 
A)  bias in inference is always bad and should be avoided at all costs, so using unbiased estimators is the only way to conduct objective inference. 
B)  unbiased estimators always have the least amount of variance of all possible estimators. 
C)  a biased estimator will almost always give very little insight into the parameter being estimated and, therefore, serves as a poor guess of the parameter's true value. 
D)  in many cases the most probable value of an unbiased estimator is the value of the parameter being estimated; thus, unbiased estimators typically converge on values near the parameter.

Question 11

When choosing between two unbiased estimators of the same parameter, the preferred estimator is:

Accepted Answer

A)  the one that is most unbiased. 
B)  the one with the smaller variance. 
C)  the one that has an expected value equal to the parameter. 
D)  Either estimator is fine, as both are unbiased. 
A)  the one that is most unbiased. 
B)  the one with the smaller variance. 
C)  the one that has an expected value equal to the parameter. 
D)  Either estimator is fine, as both are unbiased.

Question 12

Consider an arbitrary parameter δ.If we identify an estimator   such that   , then:

Accepted Answer

A)    . 
B)    is unbiased for   
C)  the maximum likelihood value for   is   
D)  the exponential value for   is   . 
A)    . 
B)    is unbiased for   
C)  the maximum likelihood value for   is   
D)  the exponential value for   is   .

Question 13

The survival times of adult mosquitoes exposed to a commonly used synthetic pesticide (Phenothrin) follow a normal distribution, with a standard deviation of 15.18 sec.A random sample of 40 mosquitoes has an average survival time of 47.5 sec.What is a 99% confidence interval for the mean survival time?

Accepted Answer

A)  (41.318, 53.682) 
B)  (41.916, 53.083) 
C)  (42.700, 52.300) 
D)  (8.399, 86.601) 
A)  (41.318, 53.682) 
B)  (41.916, 53.083) 
C)  (42.700, 52.300) 
D)  (8.399, 86.601)

Question 14

A group of biologists wish to study the life span of the common housefly.They want to estimate the mean life span with 80% confidence and a width on the interval of estimation no greater than 1 hr.How many samples should they draw if a previous study indicates that the standard deviation of life span is 2.43 hr?

Accepted Answer

A)  10 
B)  39 
C)  230 
D)  9 
A)  10 
B)  39 
C)  230 
D)  9

Question 15

A 99% confidence interval for the population mean μ is found to be (84.76, 92.17).If we were to use the same sample to construct a 95% confidence interval for this parameter, the 95% interval would be:

Accepted Answer

A)  wider than the 99% confidence interval. 
B)  the same width as the 99% confidence interval. 
C)  narrower than the 99% confidence interval. 
D)  unrelated to the 99% confidence interval in terms of center and width. 
A)  wider than the 99% confidence interval. 
B)  the same width as the 99% confidence interval. 
C)  narrower than the 99% confidence interval. 
D)  unrelated to the 99% confidence interval in terms of center and width.

Question 16

Faculty at a local university randomly sampled nine tenured faculty at their university and found that a 99% confidence interval for the mean number of years of service to achieve tenure at this university is (11.335, 15.765).Based on this interval, does a faculty member who took 16 years to achieve tenure at this university have a reason to complain?

Accepted Answer

A)  No, because the 99% confidence interval is wide and indicates it could take many years to achieve tenure. 
B)  No, because a sample of only nine faculty members is never reliable.We need to use a larger sample size. 
C)  Yes, because the interval indicates that the average time to achieve tenure should be less than 16 years with 99% confidence. 
D)  The interval does not allow us to answer this question. 
A)  No, because the 99% confidence interval is wide and indicates it could take many years to achieve tenure. 
B)  No, because a sample of only nine faculty members is never reliable.We need to use a larger sample size. 
C)  Yes, because the interval indicates that the average time to achieve tenure should be less than 16 years with 99% confidence. 
D)  The interval does not allow us to answer this question.

Question 17

A 95% confidence interval for the population proportion of professional tennis players who earn more than $2 million per year is found to be between 0.82 and 0.88.Given this information, the sample size that was used was approximately:

Accepted Answer

A)  545. 
B)  382. 
C)  233. 
D)  387. 
A)  545. 
B)  382. 
C)  233. 
D)  387.

Question 18

The cycle times for an electroplating machine are believed to be normally distributed.Twenty-one plating operations are randomly sampled, and cycle times are recorded.The sample average cycle time is 10.21 min, with a standard deviation of 0.59 min.What is a 95% confidence interval for the mean cycle time on this machine?

Accepted Answer

A)  (9.958, 10.462) 
B)  (9.941, 10.479) 
C)  (8.979, 11.441) 
D)  (9.911, 10.509) 
A)  (9.958, 10.462) 
B)  (9.941, 10.479) 
C)  (8.979, 11.441) 
D)  (9.911, 10.509)

Question 19

An unbiased estimator is:

Accepted Answer

A)  any sample statistic used to approximate a population parameter. 
B)  a sample statistic that has an expected value equal to the value of the population parameter. 
C)  a sample statistic whose value is usually less than the value of the population parameter. 
D)  any estimator whose standard error is relatively small. 
A)  any sample statistic used to approximate a population parameter. 
B)  a sample statistic that has an expected value equal to the value of the population parameter. 
C)  a sample statistic whose value is usually less than the value of the population parameter. 
D)  any estimator whose standard error is relatively small.

Question 20

A single number computed from a sample that serves as a guess for a parameter is called a(n):

Accepted Answer

A)  point estimate. 
B)  approximate estimate. 
C)  confidence estimate. 
D)  confidence interval. 
A)  point estimate. 
B)  approximate estimate. 
C)  confidence estimate. 
D)  confidence interval.

A 95% confidence interval estimate of the population mean μ can be interpreted to mean that:

Whenever a sampled population is normally distributed or whenever the conditions of the Central Limit Theorem are fulfilled, the sample mean :

Which of the following statements about the error bound B (also called the margin of error) is false?

Which of the following statements is correct?

For any arbitrary parameter , a biased estimator of is any estimate where:

Which of the following statements is false?

In general, unbiased estimators are preferred for inference because:

When choosing between two unbiased estimators of the same parameter, the preferred estimator is:

Consider an arbitrary parameter δ.If we identify an estimator such that , then:

A 99% confidence interval for the population mean μ is found to be (84.76, 92.17).If we were to use the same sample to construct a 95% confidence interval for this parameter, the 95% interval would be:

A 95% confidence interval for the population proportion of professional tennis players who earn more than $2 million per year is found to be between 0.82 and 0.88.Given this information, the sample size that was used was approximately:

An unbiased estimator is:

A single number computed from a sample that serves as a guess for a parameter is called a(n):

Why Study Statistics

An Introduction to Statistics and Statistical Inference

Tables and Graphs for Summarizing Data

Numerical Summary Measures

Probability

Random Variables and Discrete Probability Distributions

Continuous Probability Distributions

Sampling Distributions

Hypothesis Tests Based on a Single Sample

Confidence Intervals and Hypothesis Tests Based on Two Samples or Treatments

The Analysis of Variance

Correlation and Linear Regression

Categorical Data and Frequency Tables

Nonparametric Statistics

Filters

Exam 9: Confidence Intervals Based on a Single Sample

A 95% confidence interval estimate of the population mean μ can be interpreted to mean that:

Whenever a sampled population is normally distributed or whenever the conditions of the Central Limit Theorem are fulfilled, the sample mean :

Which of the following statements about the error bound B (also called the margin of error) is false?

Which of the following statements is correct?

For any arbitrary parameter , a biased estimator of is any estimate where:

Which of the following statements is false?

In general, unbiased estimators are preferred for inference because:

When choosing between two unbiased estimators of the same parameter, the preferred estimator is:

Consider an arbitrary parameter δ.If we identify an estimator such that , then:

A 99% confidence interval for the population mean μ is found to be (84.76, 92.17).If we were to use the same sample to construct a 95% confidence interval for this parameter, the 95% interval would be:

A 95% confidence interval for the population proportion of professional tennis players who earn more than $2 million per year is found to be between 0.82 and 0.88.Given this information, the sample size that was used was approximately:

An unbiased estimator is:

A single number computed from a sample that serves as a guess for a parameter is called a(n):

Why Study Statistics

An Introduction to Statistics and Statistical Inference

Tables and Graphs for Summarizing Data

Numerical Summary Measures

Probability

Random Variables and Discrete Probability Distributions

Continuous Probability Distributions

Sampling Distributions

Hypothesis Tests Based on a Single Sample

Confidence Intervals and Hypothesis Tests Based on Two Samples or Treatments

The Analysis of Variance

Correlation and Linear Regression

Categorical Data and Frequency Tables

Nonparametric Statistics

Filters