busi 2305 chap 8 smartbook
What is the most typical form of a calculated confidence interval?
Point estimate ± margin of error
The confidence coefficient equals
1 - α
The sampling distribution of estimator X 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 a sample size of at least
30
If the underlying population is not normally distributed, then by the central limit theorem, the sampling distribution of X will be approximately normally distributed if n>
30 or thirty
When calculating the required sample size for a mean CI, if n=50.13, the sample size we use is
51
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/2σ̂E)zα/2σ̂E2
In order to construct a confidence interval for μ, the sampling distribution of the estimator X must follow or approximately follow a(n) distribution
normal
In order to derive a confidence interval for μ, the estimator X must have a
normal sampling distribution.
You use sample statistics to make inferences about the unknown population
parameters
Statisticians like in their interval estimates.
precision
A confidence interval can be interpreted as a
range of values used to estimate an unknown population parameter
A confidence interval is constructed by using the point estimate as a base, to which we add and subtract the _____.
margin of error
The most practical way to reduce the margin of error is by
selecting a larger sample size.
Precision in interval estimates is implied by a(n) margin or error.
small
is a subset of the population
sample
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.
Alpha (α) is often referred to as the level
significance
When rounding a noninteger sample size, you always round
up
Match these terms from a mean confidence interval formula with their meaning.
xx Sample mean. Zα/2Zα/2 Value from the standard normal table. n Sample size. σ Standard deviation. σnσn Standard error.
If repeated samples of size n are taken from a normal population with an unknown variance, then the statistic T=______ follows the t distribution with n - 1 degrees of freedom.
x−μS/n√
As df increases, the tdf distribution becomes similar to the distribution
z
Which of the following are components of the formula for selecting n to estimate p?
zα/2 E p̂
For the 90% confidence interval, the confidence coefficient equals and α equals
0.90 0.10
A 95% confidence interval for the population mean is constructed as 6 ± 2. What is the confidence coefficient?
0.95
Which of the following characteristics describe both the z and tdftdf distributions?
asymptotic tails bell-shaped symmetric around 0
The allowed probability that an interval estimate of a population mean will not contain μ is referred to as the
level of significance.
The estimator X follows a normal distribution when the underlying population follows a distribution
normal
The formula for a mean confidence interval is valid only if X (approximately) follows a distribution
normal
consists of all items of interest in a statistical problem.
population
When estimating the population mean, the tdf distribution is used when the is unknown
population variance
Each t distribution is identified by its ______.
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 confidence interval is ______ for a greater confidence level.
wider
True or false: A confidence interval provides a range of values that should contain a population parameter with a certain level of confidence.
True
True or false: the tdftdf distribution has slightly broader tails than the z distribution.
True
In order to construct a confidence interval for the population mean μ or the population proportion p, it is essential that the sampling distributions of X and P follow, or approximately follow, a
normal
The confidence level is equal to ______.
100 x (1 - α)%
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.
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.
Which of the following are components of the formula for selecting n to estimate μ?
σ̂ E zα/2
Whenever we construct a confidence interval for the population mean, the margin of error includes the standard error of X and the
desired level of confidence.
When calculating the required sample size for a proportion CI, if you do not have an estimate of the proportion, you should use a value of
.5
A particular value of the estimator is called an
estimate
A t distribution
has slightly broader tails than the Z distribution.
A 95% confidence interval for the population mean implies that
for repeated samples, 95% of the sample means will fall within the interval.
A confidence interval is also referred to as an
interval estimate
For a given confidence level and sample size, the larger the population standard deviation, the the confidence interval.
larger
A 95% confidence interval for the population mean is constructed as 6 ± 2. The probability of error, α is
0.05
For a 95% confidence interval, α =
0.05
