unit 6: Sampling distributions Flashcards
We view statistics as random variables that have probability distributions
true
We view parameters as random variables that have probability distributions.
false
A parameter’s value is not usually known, but it is a fixed value that does not change from sample to
sample
The sampling distribution of a statistic is the probability distribution of the statistic
true
“Sampling distribution” is another name for the probability distribution of a statistic.
In repeated sampling, the value of a statistic will vary about the parameter it estimates.
true
In repeated sampling, the value of a parameter will vary about the statistic that estimates it.
false
A parameter’s value is not usually known, but it is a fixed value that does not change
from sample to sample.
The sampling distribution of µ is normal, provided n is large. Is this
statement true or false?
False. µ is a parameter, and as such it does not have a sampling distribution. (We view µ as a fixed,
unchanging value.)
The standard deviation of the sampling distribution of the sample mean depends on the value of µ
False. σX¯ = √σ/n
depends only on σ and n
We cannot possibly determine any characteristics of a statistic’s sampling distribution without
repeatedly sampling from the population.
False. We can often mathematically determine
characteristics of the sampling distribution
The sampling distribution of X¯ is always at least approximately normal for large sample sizes,
and is sometimes approximately normal for small sample sizes.
true
If the sample size is quadrupled, then the standard deviation of the sampling distribution of
the sample mean decreases by a factor of 2.
True. √σ/n
If we draw a very large sample from any population and plot a histogram of the observations,
the shape of the histogram will be approximately normal.
False. A histogram of a large number of observations sampled from a distribution will look like the distribution from which we are sampling
In practice, we usually know the true standard deviation of the sampling distribution of X¯.
false
The population standard deviation σ is almost always unknown, and so the true standard deviation of the sampling distribution of X¯ (σX¯ = √σ/n) is almost always unknown.
In practice, we usually know the true value of µ
False. In practical problems, the parameter µ
is almost always unknown
The sample mean is an unbiased estimator of the population mean.
True. E(X¯) = µ.
If we were to repeatedly sample from a population, then the distribution of the sample mean
would become approximately normal as the number of samples increases, as long as the sample
size of each sample stays constant.
False. The distribution of X¯ becomes approximately normal
as the sample size n increases (in other words, as the number of values used to calculate the mean increases).
Repeatedly sampling from a population doesn’t change the sampling distribution of
X¯.
