CH 8 ORMS 3310
What is the value of zα/2 for a 99% confidence interval for the population mean?
2.576
What is the confidence level if α = 0.10?
90%
Suppose you are constructing a confidence interval for the population mean. For a given sample size and population standard deviation, how will the width of the interval change as the confidence level increases?
It gets larger.
What is the most typical form of a calculated confidence interval?
Point estimate ± margin of error
As the population standard deviation decreases and everything else remains constant, the width of the confidence interval _____.
decreases
Which of the following are components of the formula for selecting n? Select all that apply.
desired margin of error zα/2 pˆ
A 95% confidence interval for the population mean implies that
for repeated samples, 95% of the intervals will contain the population mean.
A confidence interval can be interpreted as a
range of values used to estimate an unknown population parameter.
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
smaller sample size.
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 and the sample size.
The equation for a confidence interval for μ when the value of σ is unknown is
xx ± tα/2,df ⋅ sn√
The Greek letter ______ denotes the level of significance.
α
The required sample size for estimating a population proportion is largest when pˆp̂ equals ______.
0.50
The confidence coefficient equals
1 - α
What is the value of zα/2 for a 90% confidence interval for the population mean?
1.645
A certain type of light bulb is advertised to have a life of about 100 hours of use. With a certain level of confidence, it is advertised that the life is between 90 and 110 hours. If 100 hours is the point estimate, then the margin of error is
10 hours.
For a 95% confidence interval for the population mean, if samples of size n are drawn repeatedly from a given population, then
95% of the intervals will contain the population mean.
How does an interval estimate differ from a point estimate?
An interval estimator provides a range of values for the population parameter instead of a single value.
An estimate of the population standard deviation is necessary to determine how large of a sample size is needed to estimate the population mean. How can the population standard deviation be estimated?
Range/4
Which of the following happens when the sample size gets smaller for the unknown σ case? Select all that apply.
The t-value gets larger. The confidence interval gets wider.
How do the tdf and z distributions differ?
The tdf distribution has broader tails (it is flatter around zero).
True or false: XX follows a normal distribution in estimating the population mean.
True
A t distribution
has slightly broader tails than the Z distribution.
Alpha (α), the probability the interval does not contain the population mean, is often referred to as the
level of significance.
When constructing a confidence interval for the population mean when the population standard deviation is unknown, the degrees of freedom for the t distribution are defined as ______.
n - 1
In order to derive a confidence interval for μ, the estimator XX must have a
normal sampling distribution.
All of the following are components of the formula for selecting n to estimate μ EXCEPT:
pˆ
The most practical way to reduce the margin of error is by
selecting a larger sample size.
Precision in interval estimates is obtained by a(n) ______ margin or error.
small
Which of the following characteristics describe both the z and tdf distributions? Select all that apply.
symmetric around 0 bell-shaped asymptotic tails
The equation for a confidence interval for μ when the value of σ is known is
xx ± zα/2 ⋅ σn√
One way to reduce the margin of error is to
increase 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 standard deviation.
A confidence interval is constructed by using the point estimate as a base, to which we add and subtract the
margin of error.
In order to construct a confidence interval for μ, the sampling distribution of the estimator XX must follow or approximately follow a(n) ______ distribution.
normal
True or false: The tdf distribution has slightly broader tails than the z distribution.
True
The shape of each t distribution depends upon its ______.
degrees of freedom
A confidence interval narrows if the following is accomplished:
the chosen confidence level decreases. the sample size increases.
For a desired margin of error E, the minimum sample size required to estimate a 100(1-α)% confidence interval for the population proportion is
n = (zα/2E)zα/2E2 pˆp̂ (1 - pˆp̂)
For a desired margin of error E, the minimum sample size required to estimate a 100(1-α)% confidence interval for the population mean is
n = (zα/2σˆE)zα/2σ̂E2
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. Then the margin of error is
1 hour.
The area under the entire tdftdf distribution sums to
1 or one
A 95% confidence interval for the population mean is constructed as 6 ± 2. What is the confidence coefficient?
0.95
The sampling distribution of estimator XX follows a normal distribution when the underlying population is normally distributed and/or when the sample size is large enough. As a "rule of thumb" we use the following to check sample size:
n ≥ 30