BUS 281: Chapter 8 - Estimation
Desirable properties for an estimator include _____________. -unbiasedness, efficiency, and consistency -unbiasedness, inefficiency, and consistency -unbiasedness, efficiency, and inconsistency -bias, efficiency, and consistency
-unbiasedness, efficiency, and consistency
Suppose you are constructing a confidence interval for the population mean. For a given sample size and standard deviation, the width of the confidence interval is ______ for a greater confidence level. -the same -wider -narrower
-wider
The two pieces of information that are necessary to determine the value of tdf are _________ (check all that apply) -the sample size or degrees of freedom -the population standard deviation -the level of significance -the population mean
-the sample size or degrees of freedom -the level of significance
The Greek letter ____ denotes the level of significance. -σ -μ -β -α
-α
When constructing a confidence interval for the population mean, the factors that affect the width of the confidence interval for a given standard deviation are ___________ -the confidence level, the sample size, and the point estimate -the point estimate and the sample size -the confidence level and the sample size -the point estimate and the confidence level
-the confidence level and the sample size
An estimator is unbiased if the average value of the estimator is equal to ___________________. -the sample standard deviation -the correlation coefficient -the parameter being estimated -the sample variance
-the parameter being estimated
If the expected value of an estimator is equal to the unknown parameter being estimated, then the estimator is BEST characterized as a(n) __________________ -unbiased estimator -efficient estimator -consistent estimator -biased estimator
-unbiased estimator
When the confidence level increases 95% to 99%, the confidence interval for the population mean ___________. -narrows -stays the same -widens
-widens
All of the following are components of the formula for selecting n to estimate p EXCEPT: -zα/2 -E(desired margin of error) -p̂ -σ̂
-σ̂
A 95% confidence interval for the population proportion is calculated as (0.40, 1.00) The margin of error for this interval is ____________. a) 0.30 b) 1.96 x 0.70 c) 1.96 x 0.30 d) 0.70
a) 0.30
A random sample of 60 observations results in 42 successes. What is the point estimate of the population proportion of successes? a) 0.7 b) 1.4 c) 60 d) 40
a) 0.7
AAA batteries are advertised to have a life of about 9 hours of use. With a certain level of confidence, it is advertised that the life is between 8-10 hours. If 9 hours is the point estimate, then the margin of error is ____________. a) 2 hours b) 1 hour c) 4 hours d) 0.5 hours
b) 1 hour
A sample of 25 is drawn from a normal population. A sample mean of 50 is calculated. For a 95% confidence interval, the margin of error is 10. A 95% confidence interval for the mean is ___________. a) 50 ± 1.96(10) b) 50 ± 10 c) 50 ± 1.96(10/√25) d) 50 ± 10/√25
b) 50 ± 10
What is the value of zα/2 for a 99% confidence interval for the population mean? a) 1.96 b) 0.005 c) 2.576 d)0.01
c) 2.576
A 95% confidence interval for the population mean is constructed as 6 ± 2. What is the point estimate? a) 0.95 b) 0.05 c) 6 d) 2
c) 6
The scores of 5 randomly selected midterms are 70, 80, 65, 95, and 90. The point estimate for the population mean is ________________. a) 65 b) 78 c) 90 d) 80
b) 78
If α equals 0.05, then the confidence coefficient equals _____ a) 0.975 b) 0.025 c) 0.05 d) 0.95
d) 0.95
What is the value of zα/2 for a 90% confidence interval for the population mean? a) 0.10 b) 1.96 c) 0.05 d) 1.645
d) 1.645
The confidence level is equal to _____________. a) 100 x (α/2) % b) 100 x α % c) 100 x (1-α)/2 % d) 100 x (1-α) %
d) 100 x (1-α) %
The sample statistic x̄ is an estimator of ________. a) σ b) σ² c) p d) μ
d) μ
A confidence interval narrows if the following is accomplished: (check all that apply) -the chosen confidence level decreases -the sample size decreases -the chosen confidence level increases -the sample size increases
-the chosen confidence level decreases -the sample size increases
The mean and standard deviation are often used to describe ________ data while the proportion is a descriptive measure that can also be used for ______ data. -qualitative, quantitative -population, sample -sample, population -quantitative, qualitative
-quantitative, qualitative
The ____________ P is used as the point estimator for the ________ p. -parameter, statistic -parameter, proportion -population proportion, sample proportion -sample proportion, population proportion
-sample proportion, population proportion
Precision in interval estimates is implied by a(n) ________ margin of error -high -low -overestimated -underestimated
-low
The estimator x̄ follows a normal distribution when the underlying population follows a ________ distribution.
-normal
When estimating the population mean, the tdf distribution is used when the _____________ -size of the population is unknown -population standard deviation is known -population mean is unknown -population variance is unknown
-population variance is unknown
All of the following are components of the formula for selecting n to estimate μ EXCEPT: -zα/2 -E(desired margin of error) -p̂ -σ̂
-p̂
A point estimate is the value of the point estimator derived from a given. -sample -standard deviation -population
-sample
The most practical way to reduce the margin of error is by __________. -selecting a population with a smaller standard deviation -increasing the confidence level -using cluster random sampling rather than stratified random sampling -selecting a larger sample size
-selecting a larger sample size
Suppose you are constructing a confidence interval for the population mean. For a given confidence level and standard deviation, the width of the interval is wider for a ______________. -larger sample size -smaller point estimate -smaller sample size -larger point estimate
-smaller sample size
The variability of an estimator is often measured by its ____________. -unbiasedness -mean -correlation -standard error
-standard error
How is the consistency of an estimator defined? -An estimator is consistent if its standard error is lower than that of other unbiased estimators -A consistent estimator approaches the estimated population parameter as the sample size grows larger. population parameter -An estimator is consistent if its expected value equals the estimated population parameter -An estimator is consistent if it always gives the correct value of the estimated population parameter
-A consistent estimator approaches the estimated population parameter as the sample size grows larger. population parameter
What is the most typical form of a calculated confidence interval? -Population parameter ± margin of error -Point estimate ± standard error -Population parameter ± standard error -Point estimate ± margin of error
-Point estimate ± margin of error
How do the tdf and z distributions differ? -There is no difference between the tdf and z distributions -The tdf distribution has broader tails (it is flatter around zero) -The z distribution has broader tails (it is flatter around zero) -The z distribution has asymptotic tails, while the tdf distribution does not
-The tdf distribution has broader tails (it is flatter around zero)
True or false: A 95% confidence interval for μ implies that if numerous samples are taken from a population, 95% of the intervals will contain μ.
-True
The standard error of the sample mean is NOT affected by the ________ -variance -confidence level -standard deviation -sample size
-confidence level
Some of the desirable properties of a point estimator include _____________ (check all that apply). -consistency -unbiasedness -efficiency -autocorrelation
-consistency -unbiasedness -efficiency
An n increases, the variability of x̄ decreases implying that x̄ is a ______ -inconsistent estimator of σ -consistent estimator of σ -consistent estimator of μ -inconsistent estimator of μ
-consistent estimator of μ
Each t distribution is identified by its _______________. -degrees of freedom -significance level -standard deviation -point estimate
-degrees of freedom
Suppose you are constructing a confidence interval for the population mean. For a given sample size and standard deviation, the width of the interval is wider, for a ______________ -smaller point estimate -larger point estimate -higher confidence level -lower confidence level
-higher confidence level
An estimator is consistent if it approaches the population parameter of interest as the sample size ____________ -decreases -increases -stays the same
-increases
x̄ and p are the unbiased estimators of μ and p -if n≥30 -if the variability is small enough -if np≥5 and n(1-p)≥5 -independent of the sample size
-independent of the sample size
Suppose you are constructing a confidence interval for the population mean. For a given confidence level and sample size, the width of the interval is wider for a ______________. -larger point estimate -smaller point estimate -smaller standard deviation -larger standard deviation
-larger standard deviation
A confidence interval is constructed by using the point estimate as a base, to which we add and subtract the __________. -sample mean -confidence level -margin of error -standard error
-margin of error
In order to construct a confidence interval for μ, the sampling distribution of the estimator x̄ must follow or approximately follow a(n) ___________ distribution -normal -binomial -exponential -uniform
-normal
The sampling distribution of the sample proportion can be approximated by a normal distribution when ___________. -np ≤ 5 and n(1-p) ≤ 5 -n ≥ 30 -np ≥ 5 and n(1-p) ≥ 5 -n < 30
-np ≥ 5 and n(1-p) ≥ 5
The parameter p represents the ______________. -population margin of error -sample margin of error -sample proportion -population proportion
-population proportion