Chapter 9 ~ Sampling Distributions Flashcards
Statistic
A number that can be computed from the sample data without making use of any unknown parameters. In practise, we often use a statistic to estimate an unknown parameter.
What is the symbol for a population mean?
μ (mu)
What is the symbol for mean of a sample?
x̄ (x-bar)
Sampling Variability
The value of a statistic varies in repeated sampling. This is not fatal!
What is the symbol for a population proportion?
p
What is the symbol for a sample proportion?
p̂ (p-hat)
Sampling distribution
The distribution of values taken by the statistic in all possible samples of the same size from the same population.
Bias
The centre of the sampling distribution is not equal to the true value of the parameter.
Variability of a statistic
Described by the spread of its sampling distribution. This spread is determined by the sampling design and the size of the sample.
Larger samples –> smaller spread
What is the mean of the sampling distribution of p̂?
Exactly p
What is the standard deviation of the sampling distribution of p̂?
Sqrt(pq/n)
When can you use the formula for the standard deviation of p̂?
ONLY when the population is at least 10 times as large as the sample. (N≥10n)
What conditions must be satisfied to use the Normal approximation for the sampling distribution of p̂?
np≥10 and nq≥10
What is the mean of the sampling distribution of x̄?
Exactly μ
What is the standard deviation of the sampling distribution of x̄?
σ/sqrt(n)
If the population has a Normal distribution, then what is the shape of the sampling distribution of x̄?
Normal, regardless of the sample size
If the population shape is non-Normal (or we are not told its shape) and there is a small n, what is the shape of the sampling distribution of x̄?
Similar to the shape of the population.
If the population shape is non-Normal (or we are not told its shape) and there is a large n with a finite standard deviation, what is the shape of the sampling distribution of x̄?
Approximately Normal
What does the Central Limit Theorem state?
As long as n≥30 and there is a finite standard deviation, then the shape of the sampling distribution is approximately Normal.
Also known as the Fundamental Theorem of statistics.
Parameter
A number that describes the population.
In statistical practise, the value of a parameter is not known because we cannot examine the entire population.
