Deck 8: Large-Sample Estimation

Question 1

Which of the following best describes an unbiased estimator?

A) any sample statistic used to approximate a population parameter
B) a sample statistic which 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

Answer 1

B

Question 2

From a sample of 200 items, 12 items are defective. In this case, what will be the point estimate of the population proportion defective?

A) 0.06
B) 0.12
C) 12
D) 16.67

Answer 2

A

Question 3

Which of the following best describes the term "margin of error"?

A) It is the difference between the point estimate and the true value of the population parameter.
B) It is the critical value times the standard error of the estimator.
C) It is the smallest possible sampling error.
D) It is a measurement of the variability of the true value of the population parameter.

Answer 3

B

Question 4

Which of the following best describes an interval estimate?

A) It is a sampling procedure that matches each unit from population A with a "twin" from population B, so that any sample observation about a unit in population A automatically yields an associated observation about a unit in population B.
B) It is an estimate of a population parameter that is expressed as a range of values within which the unknown but true parameter presumably lies.
C) It is a sample statistic such that the mean of all its possible values equals the population parameter the statistic seeks to estimate.
D) It is the sum of an estimator's squared bias plus its variance.

Question 5

Which of these options is the best definition of a point estimate?

A) It is the average of the sample values.
B) It is the average of the population values.
C) It is a single value that is the best estimate of an unknown population parameter.
D) It is a single value that is the best estimate of an unknown sample statistic.

Question 6

In developing an interval estimate for a population mean for which the population standard deviation was 8, the interval estimate was 40.52 3.24. If had equalled 16, what would the interval estimate have been?

A) 40.526.48
B) 40.5211.24
C) 48.5211.24
D) 81.046.48

Question 7

A 99% confidence interval estimate for a population mean is determined to be 85.58 to 96.62. If the confidence level is reduced to 90%, what happens to the confidence interval for ?

A) It becomes wider.
B) It remains the same.
C) It becomes narrower.

Question 8

After constructing a confidence interval estimate for a population mean, you believe that the interval is useless because it is too wide. In order to correct this , what should you do?

A) increase the population size
B) increase the sample mean
C) increase the confidence coefficient
D) increase the sample size

Question 9

Which of the following must hold before one can make use of the standard normal distribution in order to construct a confidence interval estimate for the population proportion p?

A) and) are both greater than 5, whereis the sample proportion.
B) np and n(1 - p) are both greater than 5.
C) (p +) and (p -) are both greater than 1.
D) The sample size is greater than 5.

Question 10

What is the type of sample statistic that is used to make inferences about a given type of population parameter?

A) the estimator of that parameter
B) the confidence level of that parameter
C) the confidence interval of that parameter
D) the point estimate of that parameter

Question 11

Whenever a sampled population is normally distributed, or whenever the conditions of the Central Limit Theorem are fulfilled, what may be said of the sample mean ?

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

Question 12

Which of these options provides the best interpretation of a 90% confidence interval estimate of the population mean ?

A) If we repeatedly draw samples of the same size from the same population, 90% of the values of the sample meanswill result in a confidence interval that includes the population mean.
B) There is a 90% probability that the population meanwill lie between the lower confidence limit (LCL) and the upper confidence limit (UCL).
C) We are 90% confident that we have selected a sample whose range of values does not contain the population mean.
D) We are 90% confident that 10% the values of the sample meanswill result in a confidence interval that includes the population mean.

Question 13

In order to estimate the average number of kilometres that students living off-campus commute to classes every day, the following statistics were given: n = 50, = 5.21, and s = 2.48. Which of the values below would be the best point estimate of the true population mean ?

A) 1.96
B) 2.10
C) 5.21
D) 7.07

Question 14

In developing an interval estimate for a population mean, a sample of 40 observations was used. The interval estimate was 17.25 2.42. If the sample size had been 160 instead of 40, what would the interval estimate have been?

A) 17.251.21
B) 17.259.68
C) 34.504.82
D) 69.009.68

Question 15

Which of the following is NOT a part of the formula for constructing a confidence interval estimate of the population proportion?

A) a point estimate of the population proportion
B) the standard error of the sampling distribution of the sample proportion
C) the confidence coefficient
D) the value of the population proportion

Question 16

Why do those who engage in estimation insist on random sampling, rather than convenience sampling or judgment sampling?

A) because random sampling avoids the errors inherent in matched pairs sampling
B) because random sampling avoids the errors inherent in work sampling
C) because random sampling eliminates the systematic error or bias that arises in non-random sampling

Question 17

What would be the lower limit of a confidence interval, at the 95% level of confidence, for the population proportion if a sample of size 100 were to have 30 successes?

A) 0.2102
B) 0.2959
C) 0.3041
D) 0.3898

Question 18

Which of these statements is NOT a property of the confidence interval estimate of the population mean?

A) Its width narrows when the sample size increases.
B) Its width narrows when the value of the sample mean increases.
C) Its width widens when the confidence level increases.

Question 19

What is a sample statistic such that the mean of all its possible values differs from the population parameter that the statistic seeks to estimate?

A) an efficient estimator
B) an inconsistent estimator
C) a biased estimator
D) a Bayesian estimator

Question 20

Which of the following best defines statistical estimation?

A) a process of inferring the values of unknown population parameters from those of known sample statistics
B) a process of inferring the values of unknown sample statistics from those of known population parameters
C) any procedure that views the parameter being estimated not as a constant, but, just like the estimator, as a random variable
D) a sampling procedure that matches each unit from population A with a "twin" from population B so that any sample observation about a unit in population A automatically yields an associated observation about a unit in population B

Question 21

A recent survey indicates that the proportion of season ticket holders for the school hockey team who renew their seats is about 0.80. Using a 95% confidence interval and a margin of error of 0.025, what is the approximate size of the sample needed to estimate the true proportion who plan to renew their seats?

A) 689
B) 697
C) 984
D) 1179

Question 22

If the population deviation is known and we wish to estimate the population mean with 90% confidence, what is the appropriate critical z-value to use?

A) 1.28
B) 1.645
C) 1.96
D) 2.33

Question 23

If we wish to construct a 95% confidence interval estimate for the difference between two population proportions, what would the confidence level be?

A) 1.96
B) 0.95
C) 0.475
D) 0.05

Question 24

A random sample of 400 students was surveyed to determine an estimate for the proportion of all students who had attended at least three football games. The estimate revealed that between 0.372 and 0.458 of all students attended. Given this information, which of the following is the approximate value of the confidence coefficient?

A) 0.95
B) 0.92
C) 0.90
D) 0.88

Question 25

If the population deviation is known and we wish to estimate the population mean with 95% confidence, which of the following would be the appropriate critical z-value to use?

A) 1.28
B) 1.645
C) 1.96
D) 2.33

Question 26

To what does the term "confidence level" refer?

A) the absolute number of interval estimates that can be expected to contain the actual value of the parameter being estimated when the same procedure of interval construction is used again and again
B) the percentage of interval estimates that can be expected to contain the actual value of the parameter being estimated when the same procedure of interval construction is used again and again
C) the range of values among which an unknown population parameter can presumably be found
D) the sum of an estimator's squared bias plus its variance, which indicates the degree to which it is consistent, efficient, and unbiased

Question 27

Suppose you wish to estimate the difference between two population means when the population variances are known. Which critical values of z can you use to develop the 90% confidence interval estimate?

A) 2.33
B) 1.96
C) 1.645
D) 1.28

Question 28

In order to construct a 95% confidence interval estimate for the difference between the means of two normally distributed populations, where the unknown population variances are assumed not to be equal, the following summary statistics were computed from two independent samples: , , , , , and . In this case, what is the upper confidence limit?

A) 6.78
B) 18.78
C) 77.3
D) 89.3

Question 29

When two independent random samples of sizes and have been selected from populations with means and and variances and , respectively, which of the following is a property of the sampling distribution of ?

A) If the sampled populations are normally distributed, then the sampling distribution ofis exactly normal only whenandare both 30 or more.
B) If the sampled populations are normally distributed, then the sampling distribution ofis exactly normal regardless of the sizes ofand.
C) If the sampled populations are not normally distributed, then the sampling distribution ofis approximately normally distributed regardless of the sizes ofand.
D) If the sampled populations are not normally distributed, then the sampling distribution ofis approximately normally distributed only ifis 30 or more.

Question 30

In developing a confidence interval estimate for the difference between two population means, which of the following will result from an increase in the size of the sample?

A) a wider confidence interval
B) a narrower confidence interval
C) a smaller critical z-value
D) a larger critical z-value

Question 31

Which of the following are possible options when estimating a population mean , where the population standard deviation is known?

A) We may define the limits of an interval estimate ofas.
B) We may define the limits of an interval estimate ofas.
C) We may choose a smaller z-value, construct a narrower confidence interval, and achieve a higher confidence level.
D) We may choose a larger z-value, construct a wider confidence interval, and achieve a lower confidence level.

Question 32

A 95% confidence interval for the population proportion of professional tennis players who earn more than $2 million a year is found to be between 0.82 and 0.88. What was the approximate sample size used to obtain this information?

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

Question 33

What is the z-value needed to construct a 92.5% confidence interval estimate for the difference between two population proportions?

A) 2.58
B) 2.33
C) 1.96
D) 1.78

Question 34

A statistician wishes to reduce the margin of error associated with a confidence interval estimate for a population proportion p. What does she or he need to do?

A) reduce the confidence level 1 -
B) decrease the sample size n
C) take another sample
D) increase the sample size n

Question 35

If a 90% confidence interval estimate for the difference between two population proportions is to be constructed, what would the confidence coefficient be?

A) 0.90
B) 0.45
C) 0.10
D) 0.05

Question 36

What is the z-value needed to construct a 97.8% confidence interval estimate for the difference between two population proportions?

A) 2.29
B) 2.02
C) 1.96
D) 1.65

Question 37

Suppose you wish to estimate the difference between two population means when the population variances are known. Which critical value of z can you use to develop the 99% confidence interval estimate?

A) 2.575
B) 2.325
C) 1.645
D) 1.275

Question 38

What is the approximate z-value you would use if you wish to construct an 85% upper confidence bound for the population proportion p?

A) 2.33
B) 1.96
C) 1.65
D) 1.04

Question 39

What is the approximate z-value you would use if you wish to construct an 80% lower confidence bound for the population mean ?

A) 0.84
B) 1.28
C) 1.96
D) 2.33

Question 40

Suppose the population standard deviation equals 10. What is the sample size needed to estimate, with 95% confidence, a population mean within 1.5 units of its true value?

A) 171
B) 121
C) 54
D) 13

Question 41

What is the approximate z-value you would use if you wish to construct a 92% lower confidence bound for the difference between population means in the case of large samples?

A) 2.58
B) 1.65
C) 1.41
D) 1.06

Question 42

What is the approximate z-value you would use if you wish to construct a 98% upper confidence bound for the difference between population proportions?

A) 2.33
B) 2.05
C) 1.65
D) 1.41

Question 43

An estimator is a random variable calculated from a random sample that provides either a point estimate or an interval estimate for some population parameter.

Question 44

The margin of error equals the sum of an estimator's squared bias plus its variance.

Question 45

An interval estimate is an interval that provides an upper and a lower bound for a specific population parameter whose value is unknown.

Question 46

An unbiased estimator of a population parameter is an estimator whose variance is the same as the actual value of the population variance.

Question 47

The error of estimation is the difference between a statistic computed from a sample and the corresponding parameter computed from the population.

Question 48

The sample standard deviation, s, is an unbiased estimator of the population standard deviation, .

Question 49

A point estimate is a single number that is used as an estimate of a population parameter or population characteristic. It is usually derived from a random sample from the population of interest.

Question 50

If the campaign manager of the Conservative Party is interested in estimating the proportion of voters who will support the Conservative Party in the next federal election, the sample proportion, , would be the appropriate point estimate.

Question 51

A statistic is said to be unbiased if its sampling distribution has the smallest standard error.

Question 52

The maximum distance between an estimator and the true value of a parameter is called the margin of error.

Question 53

If a store manager is interested in estimating the mean amount spent per customer per visit at her store, the sample mean would be the approximate point estimate.

Question 54

A sample statistic such that the mean of all its possible values equals the population parameter that the statistic seeks to estimate is an unbiased estimator.

Question 55

The error of estimation is the distance between an estimate and the estimated parameter.

Question 56

A sample statistic such that the mean of all its possible values differs from the population parameter that the statistic seeks to estimate is a biased estimator.

Question 57

Suppose you wish to estimate a population mean based on a sample of n observations. What sample size is required if you want your estimate to be within 2 standard deviations of with probability equal to 0.95, if you know the population standard deviation is 12?

A) 239
B) 196
C) 139
D) 98

Question 58

The process of inferring the values of unknown population parameters from those of known sample statistics is called estimation.

Question 59

An estimator is unbiased if the mean of its sampling distribution is the population parameter being estimated.

Question 60

A point estimate is an estimate of a population parameter, expressed as a single numerical value.

Question 61

Increasing the sample size, n, will result in a point estimate that is closer to the true value of the population parameter.

Question 62

In developing an interval estimate for the population mean , the population standard deviation was assumed to be 6. The interval estimate was 45.0 1.5. Had equalled 12, the interval estimate would be 90 3.

Question 63

If a store manager has recently stated that she estimates the mean amount spent per customer per visit to be between $38.75 and $72.23, the numbers $38.75 and $72.23 are considered point estimates for the true population mean.

Question 64

Given that n = 49, = 75, and = 7, the lower and upper limits of the 68.26% confidence interval for the population mean are 74 and 76, respectively.

Question 65

An interval estimate is an estimate of the range for a sample statistic.

Question 66

A point estimate is a single value estimate of the value of a population parameter.

Question 67

As the sample size increases and other factors remain the same, the width of a confidence interval for a population mean tends to decrease.

Question 68

A point estimate is an estimate of the range of a population parameter.

Question 69

The margin of error 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 the upper limit of the interval on the other hand.

Question 70

In order to construct a confidence interval estimate of the population proportion p, the value of p is needed.

Question 71

The unknown parameter of a population is presumed to lie at the centre of the interval that the point estimate and margin of error create.

Question 72

The concept of margin of error applies directly when estimating the population mean, , but is not applicable when estimating the population proportion, p.

Question 73

The sample proportion is an unbiased estimator of the population proportion, p.

Question 74

A point estimate of a population parameter will likely be different from the corresponding population value due to the fact that point estimates are subject to sampling error.

Question 75

In the formula , the refers to the area in the lower tail or upper tail of the sampling distribution of the sample mean.

Question 76

The confidence coefficient is the probability that a confidence interval will enclose the estimated parameter.

Question 77

A point estimate is subject to sampling error and will almost always be different from the true value of the population parameter.

Question 78

Suppose a 95% confidence interval for the mean height of a 12-year-old male in Canada is 137 to 165 cm. It can be said that 95% of 12-year-old males in Canada have height greater than or equal to 137 cm and less than or equal to 165 cm.

Question 79

Statisticians routinely construct interval estimates by setting the point estimate as the centre of the interval and then creating a range of other possible values, known as the margin of error, below and above the centre.

Question 80

If the population variance is increased and other factors remain the same, the width of a confidence interval for the population mean tends to increase.