VIEWS: 5 PAGES: 8 POSTED ON: 8/2/2011
Confidence Intervals by Randy Gallaher Elementary Statistics Module Step 1: Select a random sample of size 30 from a normal population with mean m = 100 and standard deviation s = 20, and store the sample in list L1. (a) Press the MATH button. (b) Use the arrow keys to highlight the PRB menu. (c) Select option 6, RandNorm(. (d) Type in "100, 20, 30)". (e) Press the STOå key. (f) Press 2nd, [L1] (the 1 button). (g) Press ENTER. A sample of size 30 from a normal distribution with population mean 100 and population standard deviation 20 is now stored in list L1 of the graphing calculator. _ Step 2: Find the sample mean, x of the sample stored in list L1. (a) Press the STAT button. (b) Use the arrow keys to highlight the CALC menu. (c) Select option 1, 1-Var Stats. (d) Press ENTER. Record your value next to Sample 1 in the table on the next page. Round to one decimal place. Step 3: Calculate a 90%-level confidence interval around the sample mean found in Step 2. (a) Press the STAT button. (b) Use the arrow keys to highlight the TESTS menu. (c) Select option 7, ZInterval. (d) Press ENTER. (e) Next to "Inpt:", use the arrow keys to highlight Stats, and press ENTER. (f) Next to "s", type in our population standard deviation 20. _ (g) The correct values for x and n (from the most recently calculated 1-Var Stats) should appear automatically. If not, enter them in the appropriate places. (h) Next to "C-Level:" type in "0.9". (i) Use the arrow keys to highlight Calculate. (j) Press ENTER. The 0.90-level confidence interval for the sample mean is provided. Record your values of the lower limit and upper limit of the confidence 109 interval next to Sample 1 in the table on the next page. Round to one decimal place. Does population mean m = 100 fall within the interval? Fill in the appropriate answer next to Sample 1 in the table on the next page. Step 4: Repeat Steps 1 through 3 in order to find 19 more confidence intervals (20 total). Complete the table below. Lower limit of Upper limit of Does the _ the confidence the confidence interval contain Sample mean, x interval interval m = 100? Sample 1 Sample 2 Sample 3 Sample 4 Sample 5 Sample 6 Sample 7 Sample 8 Sample 9 Sample 10 Sample 11 Sample 12 Sample 13 Sample 14 Sample 15 Sample 16 Sample 17 110 17 Sample 18 Sample 19 Sample 20 Questions 1. How many of the 20 confidence intervals contained the population mean m = 100? __________ 2. What percentage of the 20 confidence intervals contained the population mean m = 100? _________ 3. Now compile your information with that of your classmates: (a) What was the total number of samples generated in the class? __________ (This should be 20 times the number of people in the class.) (b) What was the total number of confidence intervals containing m = 100 in the class? __________ (c) What was the percentage of confidence intervals containing m = 100 in the class? __________ 4. How do the percentages obtained in questions 2 and 3c compare to 90%? 5. If we had found 80%-level confidence intervals, what percentage of them would you expect to contain? 6. Repeat Steps 1 through 4 for an 80%-level confidence interval. A table is provided on the next page. Be sure to use "0.8" next to "C-Level:" in step 3 (h). (a) What percentage of your intervals contained m = 100? __________ (b) What was the class percentage? __________ 7. If we had found 95%-level confidence intervals what percentage of them would you expect to contain m = 100? 111 8. Repeat Steps 1 through 4 for a 95%-level confidence interval. A table is provided on the last page. Be sure to use "0.95" next to "C-Level:" in step 3 (h). (a) What percentage of your intervals contained m = 100? __________ (b) What was the class percentage? __________ 9. What does it mean to find a c-level confidence interval? 112 To be used with Question 6 (80% confidence interval) Lower limit of Upper limit of Does the _ the confidence the confidence interval contain Sample mean, x interval interval m = 100? Sample 1 Sample 2 Sample 3 Sample 4 Sample 5 Sample 6 Sample 7 Sample 8 Sample 9 Sample 10 Sample 11 Sample 12 Sample 13 Sample 14 Sample 15 Sample 16 Sample 17 Sample 18 Sample 19 Sample 20 113 114 To be used with Question 8 (95% confidence interval) Lower limit of Upper limit of Does the _ the confidence the confidence interval contain Sample mean, x interval interval m = 100? Sample 1 Sample 2 Sample 3 Sample 4 Sample 5 Sample 6 Sample 7 Sample 8 Sample 9 Sample 10 Sample 11 Sample 12 Sample 13 Sample 14 Sample 15 Sample 16 Sample 17 Sample 18 Sample 19 Sample 20 115 116