Download AP Statistics Name Activity 10 Estimating with CONFIDENCE

AP Statistics
________________________
Activity 10 Estimating with CONFIDENCE
Name
Date_________________________
That Sure Was TACKY!!!!
Materials: A thumb tack.
When you flip a FAIR coin, it is equally likely to land “HEADS” or “TAILS.” The question for
discussion. DO THUMBTACKS BEHAVE IN THE SAME WAY? Explain.
In this activity you will toss a thumbtack several times and observe whether the tack comes to
rest with the point (UP or the point down (D). The question we are trying to answer is:
What Proportion of the Time does a
Tossed
Thumbtack Settle with Its Point
UP (U)?
1. If you could toss your thumbtack over and over and over again, what proportion of all tosses
do you think would settle with the point up (U)? What is your guess? _________ = _________ is
a parameter.
2. Let’s conduct the simulation. Toss your thumbtack 50 times. Record the result of each toss (
U or D ) in the table below. The the third column, calculate the cumulative proportion of points up
(U) tosses.
Toss Outcome ( U or or D ) Cumulative Prop.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
Toss Outcome ( U or or D ) Cumulative Prop.
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
22
23
24
25
47
48
49
50
3. Construct a SCATTER PLOT of Tosses and Cumulative Proportion. Number of Tosses on
the horizontal axis and the cumulative proportion of ( U ) on the vertical axis. Connect the
consecutive points with line segments. Does the overall proportion of ( U’s ) seem to be
approaching a single value? If yes, please name the value.__________ If no, explain.
4. The n = 50 tosses is a SRS from the POPULATION of all possible tosses. The PARAMETER
is the (UNKNOWN) POPULATION proportion of tosses that would land up ( U ). What is your
BEST

ESTIMATE for
sample of 50

 ?.
We call the estimate value _________ , the proportion of ( U’s) in your
thumbtack tosses. Record your _______ = _______, How does it compare with the conjecture
you made in step number 1? Explain.

5. If you tossed your thumbtack 50 additional times, would you expect to get the same value of
________?
Explain.
If we repeat this process, the MEAN of the SAMPLING DISTRIBUTION of ________ is
equal to the POPULATION PROPORTION .
ie.

p¦ = ___________

___________ is unknown.
A question we would
like to answer is: HOW FAR WILL YOUR SAMPLE PROPORTION
______
BE FROM THE TRUE VALUE OF THE POPULATION PROPORTION
? If the sampling
distribution


is approximately normal, then the Empirical Rule, _______, _______, _______ tells us that
approximately

_________ of all sample proportion values, _______, will be within TWO (2) STANDARD
DEVIATIONS
OF

.
6. The Sampling Distribution of _______ will be approximately NORMAL if the RULE OF THUMB
#2 is satisfied. Rule of Thumb #2 id:
_____________________________________________________________________
Verify the Conditions for your SAMPLE.
7. Estimate the STANDARD DEVIATION of the SAMPLING DISTRIBUTION by computing


p¦ =
=_________ = _________
8. Construct the INTERVAL _________
sample.

_______________


_________
*
based on your
 __________*_____

_____  _____

The INTERVAL is ( _____________________ , _____________________ )

This INTERVAL is called a CONFIDENCE _________________ for the sampling distribution
of________.
The center of your confidence interval is _________.
The length of your confidence interval is __________
9. Draw the SKETCH OF A NORMAL DISTRIBUTION with your proportion mean and your
proportion standard deviation of your sample of 50 thumbtack tosses. Label the horizontal axis
and mark off a scale. Construct all of your classmates confidence intervals one after another
below the horizontal axis accurately with a ruler.
10. We have ________ samples from the same population of THUMBTACKS gave these 95%
CONFIDENCE INTERVAL. We state that in the long run, 95% of all samples give an interval
that contains the population proportion .

So, approximately 95% of the intervals, the interval _________
will contain the true population proportion

.



_________
*