Reading Assignment 2
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
For a 95% confidence interval for the population mean, if samples of size n are drawn repeatedly from a given population, then
5% of the sample means will fall outside of the corresponding confidence interval.
When calculating the required sample size for a proportion CI, if n=50.13, the sample size we use is
51
For a given confidence level and sample size, the larger the population standard deviation, the ______ the confidence interval.
Larger
The sampling distribution of the sample proportion can be approximated by a normal distribution when _____.
np ≥ 5 and n(1 - p) ≥ 5
The parameter p represents the ______.
population proportion
Statisticians like ____ in their interval estimates.
precision
The standard error of the sample mean is affected by which of the following?
standard deviation sample size variance all three.
This value of zα/2 for a 90% confidence interval for the population mean is
1.645
The confidence level is equal to
100 x (1 - α)%
The value of zα/2 for a 99% confidence interval for the population mean is
2.576
Whenever we construct a confidence interval for the population mean, the margin of error includes the standard error of x̄ and the
Desired level of confidence.
A confidence interval is also referred to as an
Interval Estimate
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.
The formula for a mean confidence interval is valid only if x̄ (approximately) follows a distribution.
normal
Alpha (α) is often referred to as the ________ level
significance
If the underlying population is not normally distributed, then by the central limit theorem, the sampling distribution of x̄ will be approximately normally distributed if n>
30
When examining the possible outcome of an election, what type of confidence interval is most suitable for estimating the current support for a candidate?
Confidence interval for the population proportion
How do the tdf and z distributions differ?
The tdf distribution has broader tails (it is flatter around zero).
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: For a given sample size n and population standard deviation σ, the lower the confidence level 100(1-α)%, the narrower the confidence interval.
True
A confidence interval is constructed by using the point estimate as a base, to which we add and subtract the _____.
margin of error
When comparing two confidence intervals, the one that has the smaller margin of error has a _____
more precise estimate of the parameter.
In order to derive a confidence interval for μ, the estimator x̄ must have a
normal sampling distribution.
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.
The probability of error α for a 99% confidence interval is
0.01
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
The probability of error α for a 90% confidence interval is
0.10
The required sample size for estimating a population proportion is largest when p̂�̂ equals
0.50
The confidence coefficient equals
1-a
The confidence coefficient equal to ______.
1-α
each t distribution is identified by its
degrees of freedom
The allowed probability that an interval estimate of a population mean will not contain μ is referred to as the
level of significance.
The point estimator for the population proportion is ______.
phat
A confidence interval narrows if the following is accomplished:
the sample size increases. the chosen confidence level decreases.
When rounding a noninteger sample size, you always round
up
When the confidence level increases from 95% to 99%, the confidence interval for the population mean ________.
widens
You use sample statistics to make inferences about the unknown population
Parameters
A ________ 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
If the minimum and maximum values of the population are available, a rough approximation for the population standard deviation is given by its ___ divided by ____
Range Four
A 95% confidence interval for the population mean implies that
for repeated samples, 95% of the sample means will fall within the interval.
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
higher confidence level.
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.
In a confidence interval, the _____ accounts for the standard error of the estimator and the desired confidence level of the interval.
Margin of Error
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 x̄ and p̂ follow, or approximately follow, a distribution.
Normal
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
When the sample size is sufficiently large, we can approximate the sampling distribution of the sample proportion using the _____ distribution.
Normal
The population proportion p is the essential descriptive measure for a _____ variable.
categorical
A 95% confidence interval for the population mean is constructed as 6 ± 2. What is the confidence coefficient?
0.95