Go to a websitehttp://digitalfirst.bfwpub.com/stats_applet/stats_applet_4_ci.html(Note that spaces in the URL are underscores_ ).

This Applet simulates taking many samples from a given population distribution, calculating the confidence interval for each sample at a selected level of confidence and then showing this interval compared to the true population value. Note if the interval calculated based on the sample "captures" the true value or not.

a)Select level of confidence =80% For sample size = 20 take 50 samples: How many do you expect will capture the true population value? _______

What % are captured on the Applet's simulation_________

b)& c) For many more samples taken at 80% level of confidence: For 100 samples: % capturing the true population value is ________

For 500 samples: ________%For 1000 samples:________%

Remember "In the long run"= Law of Large Numbers

EXTRA Question: For these 1000 samples, change the level of confidence chosen to the

other values, 90% then 95%, then 99% ...

What do you notice about:

(i)the width of the calculated confidence interval?___________________________

(ii)the % of times the intervals capture the true population value?________________

EXTRA Question: State precisely what is meant by the term "95% confidence interval"?

[Adapted from Moore et al,Q16.3, p.380(7^thed, p.378)]