# Confidence Intervals by sdfgsg234

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```									                              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

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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

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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? _________

(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?

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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?

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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

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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

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