3.10. Concepts Review#
Here we review some conceptual points from the lecture.
Please try to answer each question yourself before clicking to reveal the answer
You can discuss these points with your tutor at the computer-based tutorial session (these sessions are for discussing concepts as well as for developing Python skills)
- What are the data points in the sampling distribution of the mean?
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The sampling distribution of the mean is the expected distribution of means for many samples of size n, drawn from the same population.
- What is the shape of the sampling distribution of the mean when sample size n is large?
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By the Central Limmit Theorem, when n is large, the sampling distribution of the mean is Normal, with a mean equal to the population mean and a standard deviation equal to the standard error (population standard deviation divided by the square root of n).
- How does the spread of the sampling distribution of the mean depend on the sample size n?
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The spread (standard deviation) of the sampling distribution of the mean gets smaller as n gets large; the standard deviation of the sampling distribution is inversely proportional to the square root of n
- What is the relationship between standard error and the standard deviation?
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Standard error is the standard deviation divided by the square root of sample size n The standard error is the standard deviation of the sampling distribution.
- A student has written ‘a 95% confidence interval for the mean is the range of values that has a 95% chance of containing the mean’. What should he have written instead?
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The 95% confidence interval is an interval about the sample mean with a width such that, if a large number of samples were drawn from the same population, 95% of the calculated confidence intervals would overlap the true population mean
OR
The 95% confidence interval is an interval about the sample mean that we are 95% confident contains the true population mean - Which is wider, a 95% confidence interval or a 99% confidence interval?
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99%