1.) How many of the intervals contained the true parameter in each of the differ

Question

1.) How many of the intervals contained the true parameter in each of the different simulation?

2.) Theoretically, what percent of intervals should contain the true mean?

3.) Is there evidence from the simulation that this is approximately the same accuracy rate?

4.) Which of the above simulations represents what we do “in real life”?

Of these intervals, take the cursor and hover over the dot in the middle of the interval this represents the point estimate or sample mean. This will show you the value of the point estimate and margin of error. Displayed at the top of the intervals is the distribution of sample means. Compare the sample mean value to it’s position in the distribution of sample means.

1.) What is consistent among the sample mean values for the intervals that don’t span the true mean?

2.) How are these different from the ones that do span the true mean?

Simulate 100 confidence intervals with a 90% confidence level. Choose a sample size between 2 and 20. Look at the confidence intervals. Take note of their width. Now increase the sample size to something between 30 and 100. Look at the confidence intervals. Finally, increase the sample size to 1000. Look at the confidence intervals.

Sample size of 6:

Sample size of 44:

Sample size of 1000:

Simulate 100 confidence intervals with a 90% confidence level. Choose a sample size between 30 and 100. Look at the confidence intervals. Now increase the confidence level to 95%. Look at the confidence intervals. Finally, increase the confidence level to 99%. Look at the confidence intervals.

Sample size of 79 at 90%:

Sample size of 79 at 95%:

Sample size of 79 at 99%:

1.) How does sample size affect the confidence intervals?

2.) How does the confidence level affect the confidence intervals?

# of random samples of size n Count that contain the true mean Percent that contain the true mean Percent that don't contain the true mean 1 Sample of sizen10 Samples of size 100 Samples of 1000 Samples of size n size n 90 886 100% 70% 90% 88.6% 0% 30% 10% 11.4%

Explanation / Answer

a) Increasing the sample size decreaseas the confidence intervals as confidence intervals = 2*z * sigma/sqrt(n)

Hence, Confidence interval is inversely related to N.

b) Increasing confidence level increases the confidence interval width as the Z value increases.

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