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Section 7.4 Test Yourself
Checkpoint 7.4.1 .
What is a "sampling distribution"?
A single random sample of data drawn from a larger population.
No, a sampling distribution is created from the results of *many* samples, not just one.
A histogram of the original, raw data population.
No, that shows the population’s distribution. A sampling distribution shows the distribution of a statistic (like the mean) derived from many samples of that population.
A distribution made up of a statistic (like the mean) calculated from many repeated samples.
Correct! The chapter illustrates this by taking the mean of thousands of samples to create one distribution of those means.
The standard deviation of a population, divided by the sample size.
No, that calculation gives you the standard error, which is the standard deviation *of* the sampling distribution, not the distribution itself.
Checkpoint 7.4.2 .
What is the "standard error of the mean"?
The average of all the sample means in a sampling distribution.
No, the average of the sample means approximates the true population mean, not the standard error.
A mistake made when calculating the mean of a single sample.
No, standard error is a measure of the spread of the entire sampling distribution, not an error in one calculation.
The shortcut for finding the 97.5% cut point of a distribution.
No, the standard error is used in the shortcut calculation (mean + 2*standard error), but it is not the cut point itself.
The standard deviation of a sampling distribution of means.
Correct! The text explains this "chewy phrase" refers to the standard deviation of the distribution of sample means.
Checkpoint 7.4.3 .
What does the "law of large numbers" state will happen if you repeat a statistical process (like sampling) a very large number of times?
The distribution of the results will become perfectly bell-shaped.
No, this describes the Central Limit Theorem, which is about the shape of the distribution of sample means.
The average of the results will converge on a stable value very close to the true value.
Correct! The text states that if you run a process a large number of times, it will converge on a stable result, demonstrating this by getting closer to the true state population mean with more replications.
The number of extreme, rare events will increase.
No, the law of large numbers implies the average result becomes more stable and predictable, not more extreme.
The R `replicate()` function will start to run more slowly.
While this might be a practical side effect of doing more calculations, it is not what the statistical law describes.
Collect a sample consisting of at least 20 data points and construct a sampling distribution. Calculate the standard error and use this
to calculate the 2.5% and 97.5% distribution cut points. The data points you collect should represent instances of the same phenomenon. For instance, you could collect the prices of 20 textbooks, or count the number of words in each of 20 paragraphs.
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