Sample Estimates Flashcards
What can cause uncertainty about the sample mean?
Variability in wider population
Sample size used to calculate sample mean
Distributional shape of wider population
What two types of distribution are used to describe the shape of a histogram?
Normal and t
What shape is the normal distribution?
Bell shaped
What defines the normal distribution?
Mean (μ)
Variance (σ^2)
What is the name for the equation for the normal distribution?
Probability Density Function
What do mean and variance equal if there is a standard normal distribution?
Mean (μ) is 0
Variance (σ) is 1
What is standardisation?
Transforming a normal distribution to a standard normal by converting the normal random variable X to standard units
Z = (X-μ)/σ
How is the t-distribution indexed?
Number of observation - 1
What happens to the shape of the t-distribution if the sample size is small?
It has heavier tails compared to the normal
When is the t-distribution used instead of the normal?
Normal relies on the knowledge of σ^2 (population variance) so as we have to often estimate σ^2 from sample, t-distribution is used
What is standard error?
The standard deviation of a sampling distribution
What does a large standard error indicate?
Lots of variability between means of different samples so sample may not be representative of population (low precision)
What does a small standard error indicate?
Most means are similar to population mean so sample likely to be close reflection of the population (high precision)
How would you find the standard error of the sample mean?
Found using the standard deviation of the sample, s, and sample size, n.
s/sqrt(n)
What is the confidence interval?
The range of values (found using the t-distribution) for the true mean within which we are confident that the true parameter value lies
