Quantitative Analysis- Module 6
True or false: the tdftdf distribution is bell-shaped and symmetric around 0. True false question.
FAlse
The random variable X−μs/nX-μs/n follows the___ ___ distribution.
student, t
The standard deviation of XX is calculated as
the positive square root of the variance of XX.
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
The standard deviation of the sampling distribution of XX is calculated as ______.
σ/√n
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 ______. Multiple choice question.
n - 1
When estimating the population mean, the tdf distribution is used when the___ ___ is unknown.
population variance
Which of the following is the correct formula for the margin of error in the interval estimation of p?
zα/2 ⋅ √p(1−p)n
The confidence coefficient equal to ______.
1 - α
The confidence level is equal to ______.
100 x (1 - α)%
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 a sample size of at least
30
In a statistical problem, a population consists of
all items of interest.
Alpha (α) is often referred to as the ___ of ___.
level , significance
The allowed probability that an interval estimate of a population mean will not contain μ is referred to as the
level of significance.
A confidence interval is constructed by using the point estimate as a base, to which we add and subtract the _____.
margin of error
The formula for a mean confidence interval is valid only if XX (approximately) follows a___distribution.
normal
When the sample size is sufficiently large, we can approximate the sampling distribution of the sample proportion using the___distribution.
normal
In order to derive a confidence interval for μ, the estimator XX must have a
normal sampling distribution
The population mean μ describes a___variable.
numerical
A___consists of all items of interest in a statistical problem.
population
The probability distribution of the sample mean is commonly referred to as the _____.
sampling distribution of x
X's___ ___is simply the probability distribution derived from all possible samples of a given size from the population.
sampling, distibution
Which of the following characteristics describe both the z and tdftdf distributions?
symmetric around 0 asymptotic tails bell-shaped
For the 90% confidence interval, the confidence coefficient equals___and a equals ___.
0.90, 0.10
How does an interval estimator differ from a point estimator?
An interval estimator provides a range of values for the population parameter whereas a point estimator provides a single value.
When the information from a sample is not typical of information in the population in a systematic way, we say that___has occured.
Bias
What is the most typical form of a calculated confidence interval?
Point estimate ± margin of error
Which of these is a characteristic of a "bad" sample?
The sample is not representative of the population we are trying to describe.
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
A sample is
a subset of the population.
The population proportion p is the essential descriptive measure for a___variable.
cateorical
Each t distribution is identified by its ______. Multiple choice question.
degrees of freedom
Whenever we construct a confidence interval for the population mean, the margin of error includes the standard error of XX and the
desired level of confidence.
A t distribution
has slightly broader tails than the Z distribution.
When estimating the population mean, the tdf distribution is used when the___ ___ is unknown.
population, variance
The Greek letter ______ denotes the level of significance.
α
True or false: If we had access to data that included the entire population, then the values of the parameters would be known and no statistical inference would be required.
True
True or false: the tdftdf distribution has slightly broader tails than the z distribution.
True
A confidence interval can be interpreted as a
range of values used to estimate an unknown population parameter.
The ______ pp is used as the point estimator for the ______ p. Multiple choice question.
sample proportion, population proportion
The variance of XX, which is equal to σ2/n, is
smaller than the variance σ2 of individual observations.
The parameter p represents the ______.
population proportion
A 100(1 - α)% confidence interval for the population proportion is
pp ± zα/2 ⋅ √p(1−p)n
A statistic is a ___ ___whose value depends on the chosen random sample.
random, variable
True or false: A confidence interval provides a range of values that should contain a population parameter with a certain level of confidence.
FAlse
Which of the following statements is MOST accurate?
A parameter is a constant although its value may be unknown.
Which of the following is an example of a population parameter?
μ
In general, the variability between sample means is___ ___ the variability between observations.
less, than
X is a___variable
random
The branch of statistics that uses sample statistics to estimate a population parameter or test a hypothesis about such a parameter is BEST referred to as___statistics
inferential
A confidence interval is also referred to as an
interval, estimate
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 μ, the sampling distribution of the estimator XX must follow or approximately follow a(n)___ distribution.
normal
A population consists of all items of interest in a statistical problem, whereas a___is a subset of the population.
SAmple
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 examining the possible outcome of an election, what type of confidence interval is most suitable for estimating the current support for a candidate? Multiple choice question.
Confidence interval for the population proportion
The sampling distribution of the sample proportion can be approximated by a normal distribution when _____. Multiple choice question.
np ≥ 5 and n(1 - p) ≥ 5
For a confidence interval, the sampling distributions of the estimators for the population mean and the population proportion must be approximately___ distributed.
normrally
The estimator XX follows a normal distribution when the underlying population follows a___distribution.
normal
