Sampling variability of a mean
5 important questions on Sampling variability of a mean
If we can assume our data is roughly normally distributed, what will be the summary statistics?
2. The standard deviation (spread)
What happens when the standard deviation changes?
e.g. if the SD is smaller, the spread is reduced and the height of the distribution increases
Which inferences about the population from a single sample can we make due to theoretical relations about the sampling distribution?
- If population distribution is approximately normal
- If the sample size is large (regardless of population distribution)
2. The sampling distribution is centred around mu (mean of the population)
3. The standard deviation (spread) of the sampling distribution is known as the standard error (SE)
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How do you interpret the 95% CI?
Provides a plausible range of values for the true population mean (best estimate is the sample mean)
Will contain the true population mean 95% of the time on repeated sampling
From a single sample we can be 95% confident that the interval contains the true population mean.
What does the width of the CI depend on?
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