r16 2introduction to confidence intervals around 100 words

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Learn by Doing

Now take the opportunity to participate in this Learn by Doing discussion.

PROMPT

Use the applet to select 20 different random samples of 100 part-time college students. For each sample the applet calculates the 95% confidence interval. How many of the 20 random samples do not contain the population proportion? Is this what you expected? Explain.

Hint answer :

Answers will vary (a little). But we expect 95% (19 out of 20) of the intervals to contain the population proportion. So we expect 5% (1 out of 20) will not contain the population proportion.

Of course, the confidence level is a long run probability, so we may not get exactly these results. But in the long run with many, many repetitions, we expect 95% of the confidence intervals to contain the population proportion.

Example for student answer :

5% (1 out of 20) of the random samples do not contain the population proportion and also since only 1 out of 2 did not contain it, we expect that only 95% ( 19/20) to contain the sample proportion. Yes, this is what I expected because every time you select a random sample it is not always going to be within 2 standard error, it has to shift one way or another.