Sunday, February 17, 2008

Lecture 6 - Ch 8b - Confidence Interval for the Mean with *Unknown* Std Dev - Examples and Minitab

Example Problems
We did the following example problems (I'm not sure I captured all the details of the problems, but I think I got the important parts):

Ex1: Sample size, n=17
Find a 95% confidence interval.
A1: 0.95 is 1-alpha, so your alpha is 0.05. Therefore, you want to look up t0.025,16, which is 2.120

Ex2: Sample size, n=14
Find a 90% confidence interval.
A2: 0.90 is 1-alpha, so your alpha is 0.1. Therefore you look up t0.05,13, which is 1.771

Ex3: Sample size, n=25. xbar=50, s=8
Find a 95% confidence interval for the mean.
A3: From the t-table, you find t0.025,24 is 2.064
Therefore, the 95% confidence interval for the mean is 50 +/- 2.064 (8/sqrt(25))

Ex4: (This is problem 8.69 in the book) Sample size, n=50, xbar=5.5, s=0.1
Find a 99% confidence interval for the mean.
A4: 0.99 is 1-alpha, so alpha is 0.01. We look up t0.005,49 which is 2.68. (If your table doesn't list degrees of freedom for the one you're looking for, just use the closest one. In our case, I think we used 50 instead of 49. Close enough!)
Therefore, the 99% confidence interval for the mean is 5.5 +/- 2.68(0.1/sqrt(50))
= 5.5 +/- 0.0379
= (5.4621,5.5379)

Minitab 1 sample t screenshotUsing Minitab to find Confidence Intervals

In Minitab, pull up your data into a column. We used the teabags.mtw sample data from the textbook problem 8.69. Select Stat - Basic Statistics - 1 sample t from the menu bar. Select your data column in the Samples in columns section. Click Options and set your confidence interval.

The output from Minitab looks like this:
Variable N Mean StDev SE Mean 99% CI
Teabags 50 5.50140 0.10583 0.01497 (5.46129, 5.54151)

Unfortunately, it doesn't give us the critical value of t (which we calculated to be 2.68). But you can see that the confidence interval is pretty much the same as the answer we got above manually. I think the difference is due to the fact that Minitab used more precise values for the mean and std dev.

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