Download Chapter 11 Chi –Square Goodness of Fit Lab

Chapter 8: Confidence Interval Lab III– Heights of Women
Class Time: ________________
Names _____________________________________
_______________________________________
_______________________________________
_______________________________________
_______________________________________
ALL STUDENT WORK MUST BE TYPED. FOLLOW DIRECTIONS ON LAB GRADING OUTLINE.
Student Learning Outcomes:
The student will calculate a 90% confidence interval using the given data.
The student will examine the relationship between the confidence level and the percent of constructed
intervals that contain the population average.
Given:
TABLE I: Heights of the population of 100 Women (in Inches)
#
Height
#
Height
#
Height
#
Height
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
59.4
66.5
63.8
65.5
61.8
66.1
61.3
62.4
61.5
58.8
71.6
61.7
62.9
61.9
60.6
66.8
59.2
63.5
64.3
64.9
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
69.3
55.2
63.0
69.6
69.8
60.6
64.1
60.9
62.9
65.7
65.0
67.5
63.9
58.7
60.0
65.6
59.3
63.3
60.6
62.5
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
62.9
67.2
68.7
63.4
64.9
63.8
64.9
66.3
63.8
70.9
62.9
66.0
65.0
59.2
65.5
66.1
58.5
60.0
66.4
67.5
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
63.1
60.5
64.1
61.4
62.3
64.9
63.4
58.1
61.2
63.2
62.2
64.7
61.1
62.0
65.5
66.9
69.2
62.5
60.4
56.6
#
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
Height
58.7
65.4
65.3
63.5
64.7
57.9
65.9
62.4
58.7
67.7
64.7
60.2
64.6
61.4
58.8
69.8
62.2
59.1
66.7
62.5
1. Listed above are the heights of 100 women. Use a random number generator to randomly select 10
data values. Neatly list both your random numbers and corresponding women’s heights.
Group Data: Random Selection of 10 Women’s Heights
Random
Number
Woman’s
Height
2. Provide the correct symbols for the sample mean and sample standard deviation for your sample of
10 women’s heights. Calculate the values for the sample mean and sample standard deviation each to
one decimal point.
Sample mean: Symbol: ____________________ = Value: ________________________________
Sample standard deviation: Symbol: ________________ = Value: __________________________
3. Assume that the population standard deviation is known to be 3.3 inches. With this information,
construct a 90% confidence interval with values to one decimal point for your sample of 10 women’s
heights.
List the next calculator instruction that you used after: STAT – TESTS - _______________________
Write the confidence interval (to one decimal point) you obtained: ___________________________
4. Write the symbol for actual population mean and calculate its value to one decimal point for the
population of 100 women’s heights listed in TABLE I.
Population mean: Symbol: ____________________ = Value: ______________________________
---------------------------------------------------------------------------------------------------------------------------
Now, answer the following questions using results shown in the table below from a previous class.
These confidence intervals were calculated in the same way you calculated your confidence interval.
TABLE II
90% Confidence Intervals For Heights of Women (inches)
Constructed By A Previous Class
( 61.2 , 64.6 )
( 61.6 , 65.0 )
( 61.1 , 64.6 )
( 61.4 , 64.9 )
( 59.1 , 62.6 )
( 63.3 , 66.8 )
( 63.0 , 66.4 )
( 60.5 , 63.9 )
( 62.2 , 65.6 )
( 63.9 , 66.1 )
( 60.3 , 63.7 )
( 56.9 , 60.3 )
( 61.6 , 64.6 )
( 65.5 , 69.0 )
( 62.7 , 66.2 )
( 61.2 , 64.7 )
( 63.3 , 64.4 )
( 62.1 , 64.6 )
( 61.0 , 64.3 )
( 61.7 , 65.1 )
( 61.6 , 65.0 )
( 60.5 , 63.9 )
Discussion Questions (Using TABLE II)
1. Define the random variable, X :
2. Define the random variable, X :
3. Using Table II, the class list of confidence intervals, highlight in yellow, the confidence intervals
that actually contain the true population mean μ. How many intervals did you highlight?
Answer: ______________________________
4. Determine the percent of confidence intervals from the class list that contain the mean μ.
Show your work and estimate your answer to one decimal point.
Work Shown:
Answer: ____________
5. Is the percent of confidence intervals that contain the population mean μ close to 90%?
Check one of the following answers:
Very close ______________ Somewhat close ______________ Not very close _______________
6. Suppose we had generated 100 confidence intervals. What do you think would happen to the
percent of confidence intervals that contained the population mean compared to your answer to #4?
Discuss both the direction and value of percent. Why? (Explain clearly and completely!!!)
7. When we construct a 90% confidence interval, we say that we are 90% confident that the true
population mean lies within the confidence interval. Using complete sentences, explain what we mean
by this phrase clearly and completely.
8. Some students think that a 90% confidence interval contains 90% of the original data.
a) Go back to TABLE I and highlight in yellow each of the 100 women’s heights that lie within the
confidence interval that you generated. Count the number of heights that you highlighted.
Number of 100 women’s heights that lie within YOUR confidence interval ____________________
b) What percent of the 100 women's heights, to one decimal place, is this?
__________________
c) Is this percent close to 90%? Check off your answer.
Very close ___________ Somewhat close ____________ Not very close ____________
9. The symbol for the random variable used as the basis to create your confidence interval is: _______
10. Explain clearly and completely why it does not make sense to count original data values that lie
in a confidence interval. Think about the definition of the random variable that is being used in the
problem? This is the heart of this lab project. Be thoughtful in your response! Include the symbol for
and a discussion about the random variable being used for this problem.
11. Suppose you obtained the heights of 10 women and calculated a confidence interval from this
information. Without knowing the population mean μ, would you have any way of knowing for certain
if your interval actually contained the value of μ? Why or why not? Explain your answer clearly and
completely.