Using your TI-83/84 Calculator: Estimating a Population ...

[Pages:3]Using your TI-83/84 Calculator: Estimating a Population Mean ( Unknown) Dr. Laura Schultz

When the population standard deviation () is not known (as is generally the case), a confidence interval estimate for a population mean () is constructed using a critical value from the Student's t distribution. The TInterval calculator function will generate this confidence interval using either raw sample data or summary statistics. Remember to confirm that the population is normally distributed and/or n 30 before proceeding to generate any confidence intervals.

Generating a t interval from summary statistics:

1. Press S and > to scroll right to select the TESTS menu option.

2. Scroll down to 8:TInterval and press e.

3. To work with summary statistics, highlight STATS and press e.

4. Consider the following example. A introductory statistics class counted how many chocolate chips were in each of 42 bags of Chips Ahoy! cookies. They found x? = 1261.57 and s = 117.58 chocolate chips per bag. First, note that it is safe to apply the Central Limit Theorem because n 30. Let's use the given summary statistics to find a 95% confidence interval estimate of the mean () number of chocolate chips in all bags of Chips Ahoy! cookies. At the prompts, enter the sample mean (x?), sample standard deviation (sx), and the sample size (n). Enter 0.95 at the C-Level prompt, then highlight Calculate and press e.

5. Your calculator will give you the output screen shown to the right. The confidence interval is being reported in the form (x? - E, x? + E), which in this case is (1224.9,1298.2). Because we are working with summary statistics, we would ordinarily round to the same number of decimal places as originally given for x?. In this case, your calculator rounds the confidence limits even further. That's okay; worry about rounding only when your calculator gives more decimal places than you started with for x?.

6. What does this mean? We are 95% confident that the interval from 1224.9 to 1298.2 actually does contain the mean () number of chocolate chips in all bags of Chips Ahoy! cookies.

7. Go back and experiment with varying the confidence level (C-Level). What happens to the size of the confidence interval when you use a 90% (0.90) confidence level? A 99% (0.99) confidence level?

8. Another way to express a confidence interval estimate of is as x? - E < < x? + E, which would be 1224.9 < ................
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