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Answer directly on the worksheet. This assignment uses a scoring guide. Review the scoring guide on the last tab of the spreadsheet prior to beginning the assignment to become familiar with the expectations for successful completion.
major_assignment_2.xlsx

mat_144_confidenceintervalexplanation.xlsx

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Part 1
Requirements: Answer each question fully. Use Excel formulas with cell references. Answers must be recorded o
Possible points
Points earned
Five year inflation rate
10
Projection of expenses in Worksheet 1
10
Part 1 total
20
0
Part 2
Requirements: Answer each question fully. Use Excel formulas with cell references. Answers must be recorded o
Possible points
Points earned
Descriptive Statistics
16
Interpret Descriptive Statistics
14
Proportion calculations
10
Interpretation of proportions
10
Conversion of before well
5
Conversion of after well
5
Improvement level data set
5
Descriptive Statistics for improvement levels
10
Histogram
5
Standard error of the mean
5
Confidence interval
10
Discussion of the placement of 0
10
Part 2 total
105
0
Total of Worksheet 2
125
0
t1
references. Answers must be recorded on the worksheet.
t2
references. Answers must be recorded on the worksheet.
0%
name
Unadjusted CPI, all items for 5 years ago
Unadjusted CPI, all items for last month
Inflation rate: something that cost \$1.00 five
years ago would cost what now?
What percent increase is this?
Total budget from Worksheet 1
5 year projected budget total
Month
number
number
Year
number
number
CPI
number
number
formula
formula
number
formula
Part 1 – Budget Projection:
and you need to estimate what the cost of y
Step 1: Go to the Bureau of Labor Statistics w
bin/surveymost?cu.
Step 2: Check U.S. All items, 1982-84=100
Step 3: Click “Retrieve Data”
Use the most recent CPI value and the CPI fo
estimate the price of your trip in five years a
dget Projection:
s have decided to delay your dream vacation from Worksheet 1 for five years,
ed to estimate what the cost of your trip will be by then.
to the Bureau of Labor Statistics website at https://data.bls.gov/cgimost?cu.
eck U.S. All items, 1982-84=100
k “Retrieve Data”
ost recent CPI value and the CPI for the same month but five years earlier to
he price of your trip in five years and the five year inflation rate.
Before wells
were dug Millions of
E.Coli per ml
23
21
64
54
72
50
52
49
55
73
55
51
38
28
60
57
59
60
61
57
71
57
63
64
63
23
21
64
54
72
50
52
49
55
73
55
51
38
28
After wells
were dug Millions of
E.Coli per ml
52
3
35
44
49
35
38
10
32
52
17
37
26
0
44
40
30
42
34
33
50
40
38
43
52
0
3
35
44
49
35
38
10
32
52
17
37
26
0
Joe Lope
Before
min = formula
max = formula
mean= formula
SD = formula
sample size = formula/number
0 count = formula/number
Ratio
Percent Clean
min =
max =
mean=
SD =
sample size =
0 count =
Before
formula
Conversions
ml
29.5735
oz
1
In 24 ounces
E.coli before
formula
E. coli after
formula
After
formula
formula
formula
formula
formula/number
formula/number
After
formula
60
57
59
60
61
57
71
57
63
64
63
23
21
64
54
72
50
52
49
55
73
55
51
38
28
60
57
59
60
61
57
71
57
63
64
63
23
21
64
54
72
50
52
49
55
73
55
44
40
30
42
34
33
50
40
38
43
52
0
3
35
44
49
35
38
10
32
52
17
37
26
0
44
40
30
42
34
33
50
40
38
43
52
0
3
35
44
49
35
38
10
32
52
17
51
38
28
60
57
59
60
61
57
71
57
63
64
63
37
26
0
44
40
30
42
34
33
50
40
38
43
52
Part 2 – Data Analysis:
Enter your name in cell F1 to generate data.
You have just completed a mission to Sierra Leone. The goal of the mission was to improve the quality of
water in 100 wells in a certain region. You collected data on the E. coli count from each well before and
after your mission. You need to write a report on the success of the mission and for that you need to
perform some statistical analysis on the data. You will be looking at the data from different perspectives
to determine if the water quality has improve.
1. Calculate descriptive statistics for your data in the table provided in the Excel spreadsheet. Use the
means and standard deviations of the data to decide if it appears that there has been improvement in
water quality? (Fill in the before (F3:F8) and after (H3:H8) tables to the left for the descriptive statistics.
The data has been named before and after for your convenience in creating formulas.)
2. The water quality is “good” if the count of E coli is 0; otherwise, the water quality is still bad. Calculate
the proportion of wells with “good” water to wells whose water is not good. From this measure does it
appear that the quality of water improved? Explain and use the proportions that you calculated. (In G11
and H11 calculate the percent Clean for before and after.)
3. Look at well #1 (B2 and C2) in your data. If you drank 24oz of water how many E.coli would you ingest if
you drank from the well before the mission? After the mission? (In E19 and G19 calculate how many E.coli
would you ingest if you drank 24 oz. of water from Well 1 before the mission and after the mission.)
ou ingest if
many E.coli
Original
Before
Data
78
19
32
125
53
68
4
106
38
36
4
17
43
23
32
49
36
2
33
58
75
82
80
70
79
73
76
72
72
70
84
81
69
85
100
70
74
63
Original
After
Data
67
4
23
110
41
42
10
79
6
16
14
5
9
3
8
28
18
21
22
25
59
63
60
52
50
66
54
42
55
53
54
62
59
52
69
57
45
39
76
78
87
71
83
71
75
76
63
70
65
83
76
78
76
68
77
75
67
74
86
85
72
73
59
72
64
67
79
64
86
74
83
81
70
71
68
76
72
71
86
86
88
78
73
84
78
60
75
64
41
67
56
57
58
39
38
50
59
48
59
49
47
51
58
53
45
58
67
48
65
43
55
25
48
55
33
65
53
61
55
47
54
54
64
55
55
77
62
67
59
45
57
53
77
88
83
70
65
74
73
79
87
79
77
66
73
85
77
57
68
61
32
48
52
53
58
59
57
55
52
58
63
55
Random
seed
numbers
9
17
25
33
41
49
57
65
73
81
89
97
5
13
21
29
37
45
53
61
69
77
85
93
1
9
17
25
33
41
49
57
65
73
81
89
97
5
8
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
63
4
17
110
38
53
0
91
23
21
0
2
28
8
17
34
21
0
18
43
60
67
65
55
64
58
61
57
57
55
69
66
54
70
85
55
59
48
52
0
8
95
26
27
0
64
0
1
0
0
0
0
0
13
3
6
7
10
44
48
45
37
35
51
39
27
40
38
39
47
44
37
54
42
30
24
13
21
29
37
45
53
61
69
77
85
93
1
9
17
25
33
41
49
57
65
73
81
89
97
5
13
21
29
37
45
53
61
69
77
85
93
1
9
17
25
33
41
49
57
65
73
81
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
61
63
72
56
68
56
60
61
48
55
50
68
61
63
61
53
62
60
52
59
71
70
57
58
44
57
49
52
64
49
71
59
68
66
55
56
53
61
57
56
71
71
73
63
58
69
63
45
60
49
26
52
41
42
43
24
23
35
44
33
44
34
32
36
43
38
30
43
52
33
50
28
40
10
33
40
18
50
38
46
40
32
39
39
49
40
40
62
47
52
44
30
42
38
89
97
5
13
21
29
37
45
53
61
69
77
85
93
1
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
62
73
68
55
50
59
58
64
72
64
62
51
58
70
62
42
53
46
17
33
37
38
43
44
42
40
37
43
48
40
Before
wells
were dug Millions of
E.Coli per
ml
After
wells
were dug Millions of Improvement
E.Coli per Level:
ml
Before – After
23
21
64
54
72
50
52
49
55
52
3
35
44
49
35
38
10
32
IMPROVEMENTS
min =
formula
max =
formula
mean=
formula
SD =
formula
SE =
formula
73
55
51
38
28
60
57
59
60
61
57
71
57
63
64
63
23
21
64
54
72
50
52
49
55
73
55
51
38
52
17
37
26
0
44
40
30
42
34
33
50
40
38
43
52
0
3
35
44
49
35
38
10
32
52
17
37
26
Low
High
Bins
Formula/NumberFormula/Number
words or formula
Formula/NumberFormula/Number
words or formula
Formula/NumberFormula/Number
words or formula
Formula/NumberFormula/Number
words or formula
Formula/NumberFormula/Number
words or formula
Formula/NumberFormula/Number
words or formula
Formula/NumberFormula/Number
words or formula
Formula/NumberFormula/Number
words or formula
Formula/NumberFormula/Number
words or formula
Formula/NumberFormula/Number
words or formula
Formula/NumberFormula/Number
words or formula
(remember to create the Histogram, too).
Frequency Distribution
95% Confidence Interval
Lower number
to
Higher number
formula
to
formula
28
60
57
59
60
61
57
71
57
63
64
63
23
21
64
54
72
50
52
49
55
73
55
51
38
28
60
57
59
60
61
57
71
57
63
64
63
23
21
64
54
72
50
52
49
55
73
0
44
40
30
42
34
33
50
40
38
43
52
0
3
35
44
49
35
38
10
32
52
17
37
26
0
44
40
30
42
34
33
50
40
38
43
52
0
3
35
44
49
35
38
10
32
52
55
51
38
28
60
57
59
60
61
57
71
57
63
64
63
17
37
26
0
44
40
30
42
34
33
50
40
38
43
52
ncy Distribution
Cumulative
Frequency
Formula
Formula
Formula
Formula
Formula
Formula
Formula
Formula
Formula
Formula
Formula
eate the Histogram, too).
Part 2 – Data Analysis:
You have just completed a mission to Sierra Leone. The goal of the mission was to impro
100 wells in a certain region. You collected data on the E. coli count from each well befo
(Q2). You need to write a report on the success of the mission and for that you need to p
analysis on the data. You will be looking at the data from different perspectives to deter
has improved.
Frequency
Formula
Formula
Formula
Formula
Formula
Formula
Formula
Formula
Formula
Formula
Formula
4. Since you collected water from the same source twice it makes sense to analyze the a
well’s water quality improved. Calculate a data set that would measure the improveme
the descriptive statistics for that data set, including both the standard deviation and st
data set. (see section 3.5 of the textbook). Make a frequency distribution and histogram
the improvement in the water quality of each well in column D. (Difference in Level of e.
two tables to the left and make a histogram of the improvement levels. (NOTE: The Stan
data set is not the same as the standard error. Use the formulas from section 3.5 of the t
standard error of the means.))
5. You have calculated one sample of 100 wells and their improvement levels. If you cou
samples of 100 wells, the distribution of all of those sample means would be a normal di
3.5). Find the 95% confidence interval of that distribution, using your sample mean as t
the standard error of your sample as the population standard deviation. (Calculate the
of the sampling distribution in cells F24 and H24.)
6. Suppose that 0 was inside of the 95% confidence interval. From that measure,
water became cleaner? Why or why not? Suppose that 0 was outside the 95% confidenc
measure, could you conclude that the water became cleaner? Why or why not?
he mission was to improve the quality of water in
unt from each well before (Q1) after your mission
d for that you need to perform some statistical
nt perspectives to determine if the water quality
s sense to analyze the amount by which each
measure the improvement level of each well, and
andard deviation and standard error (SE) for the
stribution and histogram for your data. (Calculate
(Difference in Level of e. Coli.) Then, fill out the
levels. (NOTE: The Standard deviation of this
from section 3.5 of the text to calculate the
ement levels. If you could take all possible
ns would be a normal distribution. (see section
g your sample mean as the population mean and
(Calculate the 95% confidence interval
m that measure, could you conclude that the
tside the 95% confidence interval. From that
Why or why not?
Here is one sample from the before data. Hit to get a new
Samples from the after data
sample.
mean is found. This is repeat
distribution. The normal dist
Before
the mean of the after data a
25
standard deviation of the aft
20
root of the number of sampl
background. The 95% confide
15
red coloring on the normal di
10
mean + 1.96*SE). The meanin
5
the sampling distribution sho
>100
100
95
90
85
80
75
70
65
60
55
50
45
40
35
30
25
20
15
10
5
0
0
Here is one sample from the after data. Hit to get a new sample.
After
25
20
1000 mean counts
0.2
0.18
0.16
0.14
0.12
0.1
0.08
0.06
0.04
0.02
0
15
10
Mean of samplin
Standard Deviation of
5
100
>100
95
90
85
80
75
70
65
60
55
50
45
40
35
30
25
20
15
10
5
0
0
Here is another perspective. 100 samples were drawn from the After Data. A 95% CI
expect 95% of these CI’s to contain the true population mean. Hit to regenerate.
100 CI’s computed from Samples of size 100 from the After D
72
67
62
57
52
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59
52
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59
Population Mean
%CI’s that contain the mean:
95%
Each CI is formed by finding the me
standard deviation of the sample (S
of samples). The CI is computed as (
A good intuition for the CI: The mean is a point estimate. You take a sample of the population,
as an estimate for the population mean. Why should this estimate be any good, after all, you just
is an interval estimate, a 95% CI is an interval obtained from a sample and you interpret this as:
population mean is in the interval.” You are not predicting a specific mean for the population, inst
possible values for the population mean and you are able to quantify how certain you are that the
that interval.
Samples from the after data of size 100 are taken and the
mean is found. This is repeated 1000 times to get a sampling
distribution. The normal distribution which has mean equal to
the mean of the after data and standard deviation equal to the
standard deviation of the after data divided by the square
root of the number of samples, this is the SE, is shown in the
background. The 95% confidence interval is indicated by the
red coloring on the normal distribution, this is (mean – 1.96*SE,
mean + 1.96*SE). The meaning should be clear, about 95% of
the sampling distribution should occur in this interval.
1000 mean counts for samples of size 100
Mean of sampling distribution: 65.87
Standard Deviation of Sampling Dist: 2.277169168
m the After Data. A 95% CI was created for each. We should
mean. Hit to regenerate.
f size 100 from the After Data
59 61 63 65 67 69 71 73 75 77 79 81 83 85 87 89 91 93 95 97 99
59 61 63 65 67 69 71 73 75 77 79 81 83 85 87 89 91 93 95 97 99
I is formed by finding the mean (M) of the sample and then the
rd deviation of the sample (SD). SE is computed as SD/sqrt(#
ples). The CI is computed as (M – 1.96*SE, M + 1.96*SE)
e a sample of the population, take the sample mean and use this
be any good, after all, you just have one random sample. The CI
ple and you interpret this as: “I am 95% certain that the actual
c mean for the population, instead you are finding an interval of
y how certain you are that the true population mean is inside