STATS DAT 565 week 3 Exam Questions with Correct Answers Latest Update 2025-2026
For a population with σ = 10, an x calculated from a sample of 36 observations will have a
standard error = - Answers 1.67
The CLT applies to populations with distributions - Answers that are not normal or are unknown.
The probability distribution of the sample mean is commonly referred to as the distribution of
the sample mean. - Answers sampling
If we were to sample (size = n) repeatedly from a given population, the average value of the
sample means will equal - Answers the population mean.
The standard deviation of x is called the - Answers standard error of x
The standard error decreases - Answers as n increases.
The central limit theorem states that the sampling distribution of x will approach a distribution
as the sample size n increases. - Answers normal
The sampling distribution of a sample mean refers to - Answers The probability distribution of
all x values calculated from all possible samples of size n.
Because x is an unbiased estimator for μ - Answers E(x) = μ
The standard deviation of x is calculated as - Answers σn
The normal distribution approximation for x is typically considered appropriate when the sample
size n ≥ - Answers 30
For a normal population with μ = 25 and σ = 5, we would expect 95% of all x's calculated from n
=9 to fall between _____ and _____. (Round to two decimals.) - Answers 21.73 and 28.27
The CLT states that the sampling distribution of x will approach ________ as n increases. -
Answers N(μ, σn)
The equation for a confidence interval for μ when the population standard deviation is known is
- Answers x± zα/2 σn
The three characteristics required to properly describe a sampling distribution are - Answers
variance
mean
shape
A confidence interval provides a range of values that for a given level of confidence contains -
Answers the population parameter.
, The expected value of x is equal to the __The expected value of the sample proportion, p, is the
population mean. - Answers population
A sample size less than 30 might be sufficient for the sampling distribution on x to be
considered approximately normal if - Answers the population distribution is symmetric.
When applying the CLT to define an interval within which we expect 95% of all sample means to
fall we would use a z = _______. - Answers 1.96
The two components of a confidence interval are the point ± the of error. - Answers estimate
margin
For a 90% confidence interval the value for zα/2 is _____. (Round to three decimals.) - Answers
1.645
Precision is directly linked with the width of a confidence interval. The smaller the interval, the
the precision. - Answers greater
A confidence interval - Answers is a range of values used to estimate an unknown population
parameter.
x will have a normal distribution if X is normally distributed. However the sample size - Answers
n can be any size
By increasing the sample size, n, and keeping the confidence level the same, the width of the
confidence interval - Answers will decrease
The desired confidence level is often called _____. - Answers 1-α
A confidence interval to estimate μ will be more precise for a population with ______ variation
than a population with _______ variation, keeping n and 1-α constant. - Answers less; greater
True or false: A 95% confidence interval implies that the probability that μ falls in that interval is
0.95. - Answers False
The sampling distribution of a sample mean is ________ if the population from which the sample
is drawn is normally distributed. - Answers normal
True or false: For a given sample size n and population standard deviation σ, a lower confidence
level implies a narrower confidence interval. - Answers True
AAA batteries are advertised to have a life of about 9 hours of use. With a certain level of
confidence, you can advertise that the life is between 8-10 hours. In this example, 9 hours is the
point estimate and what is the margin of error? - Answers 1 hour
When constructing a confidence interval from a non-normal population with known variance, the
For a population with σ = 10, an x calculated from a sample of 36 observations will have a
standard error = - Answers 1.67
The CLT applies to populations with distributions - Answers that are not normal or are unknown.
The probability distribution of the sample mean is commonly referred to as the distribution of
the sample mean. - Answers sampling
If we were to sample (size = n) repeatedly from a given population, the average value of the
sample means will equal - Answers the population mean.
The standard deviation of x is called the - Answers standard error of x
The standard error decreases - Answers as n increases.
The central limit theorem states that the sampling distribution of x will approach a distribution
as the sample size n increases. - Answers normal
The sampling distribution of a sample mean refers to - Answers The probability distribution of
all x values calculated from all possible samples of size n.
Because x is an unbiased estimator for μ - Answers E(x) = μ
The standard deviation of x is calculated as - Answers σn
The normal distribution approximation for x is typically considered appropriate when the sample
size n ≥ - Answers 30
For a normal population with μ = 25 and σ = 5, we would expect 95% of all x's calculated from n
=9 to fall between _____ and _____. (Round to two decimals.) - Answers 21.73 and 28.27
The CLT states that the sampling distribution of x will approach ________ as n increases. -
Answers N(μ, σn)
The equation for a confidence interval for μ when the population standard deviation is known is
- Answers x± zα/2 σn
The three characteristics required to properly describe a sampling distribution are - Answers
variance
mean
shape
A confidence interval provides a range of values that for a given level of confidence contains -
Answers the population parameter.
, The expected value of x is equal to the __The expected value of the sample proportion, p, is the
population mean. - Answers population
A sample size less than 30 might be sufficient for the sampling distribution on x to be
considered approximately normal if - Answers the population distribution is symmetric.
When applying the CLT to define an interval within which we expect 95% of all sample means to
fall we would use a z = _______. - Answers 1.96
The two components of a confidence interval are the point ± the of error. - Answers estimate
margin
For a 90% confidence interval the value for zα/2 is _____. (Round to three decimals.) - Answers
1.645
Precision is directly linked with the width of a confidence interval. The smaller the interval, the
the precision. - Answers greater
A confidence interval - Answers is a range of values used to estimate an unknown population
parameter.
x will have a normal distribution if X is normally distributed. However the sample size - Answers
n can be any size
By increasing the sample size, n, and keeping the confidence level the same, the width of the
confidence interval - Answers will decrease
The desired confidence level is often called _____. - Answers 1-α
A confidence interval to estimate μ will be more precise for a population with ______ variation
than a population with _______ variation, keeping n and 1-α constant. - Answers less; greater
True or false: A 95% confidence interval implies that the probability that μ falls in that interval is
0.95. - Answers False
The sampling distribution of a sample mean is ________ if the population from which the sample
is drawn is normally distributed. - Answers normal
True or false: For a given sample size n and population standard deviation σ, a lower confidence
level implies a narrower confidence interval. - Answers True
AAA batteries are advertised to have a life of about 9 hours of use. With a certain level of
confidence, you can advertise that the life is between 8-10 hours. In this example, 9 hours is the
point estimate and what is the margin of error? - Answers 1 hour
When constructing a confidence interval from a non-normal population with known variance, the
