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Answer directly on the worksheet.
This assignment uses a scoring guide. Review the scoring guide on the first tab of the spreadsheet prior to beginning the assignment to become familiar with the expectations for successful completion.
Please note that the Confidence Interval Explanation document is provided for reference and assistance with Major Assignment 2.
Part 1
Requirements: Answer each question fully. Use Excel formulas with cell references. Answers must be rec
Possible points
Points earned
Five year inflation rate
10
Projection of expenses in Major Assignment 1
10
Part 1 total
20
0
Part 2
Requirements: Answer each question fully. Use Excel formulas with cell references. Answers must be rec
Possible points
Points earned
Descriptive Statistics
16
Interpret Descriptive Statistics
14
Proportion calculations
10
Interpretation of proportions
10
Conversions
10
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
1
h cell references. Answers must be recorded on the worksheet.
Comments
2
h cell references. Answers must be recorded on the worksheet.
Comments
0%
Input your name below:
Amanda
Name!
Unadjusted CPI, all items for 5 years ago
Unadjusted CPI, all items for last month
What is the 5 year inflation rate, that is
percent increase in your CPI values?
If something cost $1.00 five years ago, what
would it cost now?
Total budget from Major Assignment 1
5 year projected budget total
Color Key:
formula
text/number
Month
January
January
Year
1
CPI
You should just use the budget information
2015 233,707 CPI values, here are the instructions:
2020 257,971 Step 1: Go to the Bureau of Labor Statistics w
Step 2: Check the box next to “U.S. city aver
Step 3: Click “Retrieve Data”
10%
Use the most recent CPI value and the CPI fo
earlier to compute the 5 year inflation rate.
$0,10
the price of your trip five years from now.
$5.784,00
CPI Data Link
Like Topic 4 DQ 1
just use the budget information from Major Assignment 1. For the
here are the instructions:
to the Bureau of Labor Statistics website at the link below.
eck the box next to “U.S. city average, All items – CUUR0000SA0”
k “Retrieve Data”
ost recent CPI value and the CPI for the same month but five years
ompute the 5 year inflation rate. Use this inflation rate to estimate
f your trip five years from now.
CPI Data Link
Enter your name in cell A2 of “Part 1 – Inflation” to
generate data.
Before wells After wells
were dug
were dug
E.Coli per ml E.Coli per ml
19
27
37
10
32
24
32
22
24
6
14
22
23
11
14
26
27
31
33
0
2
35
44
5
19
41
44
12
31
18
34
22
26
11
26
11
18
15
33
8
16
9
33
9
14
12
24
3
10
14
31
19
36
3
24
53
49
0
4
3
17
36
31
1
14
7
19
20
34
21
27
0
0
7
23
0
YOUR NAME:
From Part 1 A1
Amanda
Before
min = formula
max = formula
mean= formula
SD = formula
# of wells tested = formula
# of wells with 0 E coli = formula
Ratio
Percent Clean
Conversions
ml
29,5735
In 24 ounces
E.coli before
formula
13
33
26
44
26
14
37
31
5
18
13
10
46
25
33
16
29
35
32
39
14
26
28
23
26
17
35
32
10
29
41
30
26
25
43
30
22
27
38
27
26
2
27
22
25
30
25
17
27
34
20
23
21
20
0
18
9
0
44
11
17
16
16
14
19
32
9
26
19
0
7
10
22
18
11
35
27
18
13
14
21
27
4
31
28
15
9
0
0
17
12
11
26
29
37
3
22
15
8
14
24
19
13
15
11
11
18
30
27
23
12
33
40
28
27
36
26
20
20
28
36
38
34
16
29
24
0
14
15
0
10
21
0
11
11
1
0
10
16
18
8
12
15
31
10
12
31
10
15
1
22
31
26
16
0
18
18
0
Part 2 – Data Analysis:
Enter your name in cell A2 of “Part 1 – Infla
You have just completed a mission to Sierra
quality of water in the wells in a certain reg
well before and after your mission. You nee
for that you need to perform some statistic
from different perspectives to determine if
A2 of “Part 1 – Inflation” to
ate data.
After
min =
max =
mean=
SD =
# of wells tested =
# of wells with 0 E coli =
Before
formula
versions
formula
formula
formula
formula
formula
formula
Recall Topic 1 DQ 2
After
formula
1. Calculate descriptive statistics for your da
the statistics including mean, max and stan
there has been improvement in water quali
statistics to obtain full marks. (Fill in the be
descriptive statistics. The data has been nam
formulas.)
Answer Question 1 below:
Color Key:
oz
1
4 ounces
E. coli after
formula
formula
text/number
2. The water quality is “good” if the count o
Calculate the proportion of wells with “goo
measure does it appear that the quality of
you calculated. (In G11 and H11 calculate th
Answer Question 2 below:
3. Look at well #1 (B2 and C2) in your data.
ingest if you drank from the well before the
how many E.coli would you ingest if you dra
after the mission.)
Nothing to answer here!
ata Analysis:
r name in cell A2 of “Part 1 – Inflation” to generate data.
ust completed a mission to Sierra Leone. The goal of the mission was to improve the
water in the wells in a certain region. You collected data on the E. coli count from each
e and after your mission. You need to write a report on the success of the mission and
ou need to perform some statistical analysis on the data. You will be looking at the data
rent perspectives to determine if the water quality has improve.
e descriptive statistics for your data in the table provided in the Excel spreadsheet. Use
ics including mean, max and standard deviations of the data to decide if it appears if
been improvement in water quality? This requires a thorough discussion of these
o obtain full marks. (Fill in the before (F3:F8) and after (H3:H8) tables to the left for the
e statistics. The data has been named before and after for your convenience in creating
nswer Question 1 below:
er quality is “good” if the count of E coli is 0; otherwise, the water quality is still bad.
the proportion of wells with “good” water to wells whose water is not good. From this
does it appear that the quality of water improved? Explain and use the proportions that
ated. (In G11 and H11 calculate the percent Clean for before and after.)
nswer Question 2 below:
well #1 (B2 and C2) in your data. If you drank 24oz of water how many E.coli would you
ou drank from the well before the mission? After the mission? (In E19 and G19 calculate
E.coli would you ingest if you drank 24 oz. of water from Well 1 before the mission and
mission.)
Nothing to answer here!
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
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
63
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
39
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
78
77
88
83
70
65
74
73
79
87
79
77
66
73
85
77
53
57
68
61
32
48
52
53
58
59
57
55
52
58
63
55
Enter your name in cell A2 of
“Part 1 – Inflation” to generate data.
Before wells
were dug
E.Coli per ml
After wells
were dug
E.Coli per ml
Improvement
Data:
Before – After
19
37
32
32
24
14
23
14
27
33
2
27
10
24
22
6
22
11
26
31
0
35
44
19
44
31
34
26
26
18
33
16
33
14
24
10
31
36
24
49
4
17
31
14
19
34
27
0
5
41
12
18
22
11
11
15
8
9
9
12
3
14
19
3
53
0
3
36
1
7
20
21
0
7
All computations use
column D, the
“Improvement” data.
min = formula
max = formula
mean= formula
SD = formula
count = formula
SE = formula
Histogram – Width
Bin Width
formula
Frequency Distribution
Low
formula
formula
formula
formula
formula
formula
formula
formula
formula
formula
formula
High
Bins
formula
auto
formula
auto
formula
auto
formula
auto
formula
auto
formula
auto
formula
auto
formula
auto
formula
auto
formula
auto
formula
auto
Remember to create the Histogram.
95% Confidence Interval
Lower number
to
Higher number
formula
to
formula
23
13
33
26
44
26
14
37
31
5
18
13
10
46
25
33
16
29
35
32
39
14
26
28
23
26
17
35
32
10
29
41
30
26
25
43
30
22
27
38
27
26
2
27
22
25
0
17
27
34
20
23
21
20
0
18
9
0
44
11
17
16
16
14
19
32
9
26
19
0
7
10
22
18
11
35
27
18
13
14
21
27
4
31
28
15
9
0
0
17
12
11
30
25
37
3
22
15
8
14
24
19
13
15
11
11
18
30
27
23
12
33
40
28
27
36
26
20
20
28
36
38
34
16
29
24
26
29
0
14
15
0
10
21
0
11
11
1
0
10
16
18
8
12
15
31
10
12
31
10
15
1
22
31
26
16
0
18
18
0
Part 2 – Data Analysis:
You have just completed a mission to Sierra Leone. The goal of the mission was
wells in a certain region. You collected data on the E. coli count from a sample
mission. You need to write a report on the success of the mission and for that y
statistical analysis on the data. You will be looking at the data from different pe
water quality has improved.
Color Key:
formula
text/number
4. Since you collected water from the same source twice it makes sense to ana
well’s water quality improved. Calculate a data set that would measure the ch
each well, and the descriptive statistics for that data set, including both the s
error (SE) for the data set. (see section 3.5 of the textbook and the additional E
with this major assignment). Make a frequency distribution and histogram for
improvement in the water quality of each well in column D. (Difference in Lev
tables to the left and make a histogram of the improvement levels. (NOTE: The
is not the same as the standard error. Use the formulas from section 3.5 of the
error of the means.))
ncy Distribution
Cumulative
Frequency
formula
formula
formula
formula
formula
formula
formula
formula
formula
formula
formula
create the Histogram.
Frequency
formula
formula
formula
formula
formula
formula
formula
formula
formula
formula
formula
5. You have calculated one sample of wells and their improvement levels. If yo
wells of the, the distribution of all of those sample means would be a normal d
the 95% confidence interval of that distribution, using your sample mean as t
standard error of your sample as the population standard deviation. (Calcula
the sampling distribution in cells F30 and H30.)
6. Recall that a 95% confidence interval shows a range of values that is 95% like
your 95% confidence interval for the average improvement level is (14, 18), it w
likely to be in the range (14, 18). (See the additional Excel document provided a
Histogra
Now answer each of these questions:
a) Look at the mean for your improvement data, based on this what would you
wells.
b) Look at the confidence interval you calculated–is the value 0 inside or outsid
c) If the value 0 is outside and less than your 95% confidence interval, can you
cleaner?
d) What if the value 0 were inside your confidence interval? Could you conclud
Answer Question 6 (a):
Answer Quastion 6 (b):
Answer Question 6 (c):
Answer Question 6 (d):
eone. The goal of the mission was to improve the quality of water in
n the E. coli count from a sample of wells before and after your
ccess of the mission and for that you need to perform some
king at the data from different perspectives to determine if the
ource twice it makes sense to analyze the amount by which each
ta set that would measure the change in the number of E. coli in
hat data set, including both the standard deviation and standard
the textbook and the additional Excel document provided along
cy distribution and histogram for your data. (Calculate the
ell in column D. (Difference in Level of e. Coli.) Then, fill out the two
e improvement levels. (NOTE: The Standard deviation of this data set
e formulas from section 3.5 of the text to calculate the standard
nd their improvement levels. If you could take all possible samples of
mple means would be a normal distribution. (see section 3.5). Find
ion, using your sample mean as the population mean and the
tion standard deviation. (Calculate the 95% confidence interval of
0.)
s a range of values that is 95% likely to contain the true value of a parameter. For example, if
improvement level is (14, 18), it would mean that the true average improvement level is 95%
itional Excel document provided along with this major assignment for more details.)
ata, based on this what would you say about the change in the quality of water in the tested
ted–is the value 0 inside or outside your confidence interval?
95% confidence interval, can you conclude (with 95% confidence) that the water became
ence interval? Could you conclude (with 95% confidence) that the water became cleaner?
Part 1
Requirements: Answer each question fully. Use Excel formulas with cell references. Answers must be rec
Possible points
Points earned
Five year inflation rate
10
Projection of expenses in Major Assignment 1
10
Part 1 total
20
0
Part 2
Requirements: Answer each question fully. Use Excel formulas with cell references. Answers must be rec
Possible points
Points earned
Descriptive Statistics
16
Interpret Descriptive Statistics
14
Proportion calculations
10
Interpretation of proportions
10
Conversions
10
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
1
h cell references. Answers must be recorded on the worksheet.
Comments
2
h cell references. Answers must be recorded on the worksheet.
Comments
0%
Input your name below:
Amanda
Name!
Unadjusted CPI, all items for 5 years ago
Unadjusted CPI, all items for last month
What is the 5 year inflation rate, that is
percent increase in your CPI values?
If something cost $1.00 five years ago, what
would it cost now?
Total budget from Major Assignment 1
5 year projected budget total
Color Key:
formula
text/number
Month
January
January
Year
1
CPI
You should just use the budget information
2015 233.707 CPI values, here are the instructions:
2020 257.971 Step 1: Go to the Bureau of Labor Statistics w
Step 2: Check the box next to “U.S. city aver
Step 3: Click “Retrieve Data”
10%
Use the most recent CPI value and the CPI fo
earlier to compute the 5 year inflation rate.
$0.10
the price of your trip five years from now.
$5,784.00
CPI Data Link
Like Topic 4 DQ 1
just use the budget information from Major Assignment 1. For the
here are the instructions:
to the Bureau of Labor Statistics website at the link below.
eck the box next to “U.S. city average, All items – CUUR0000SA0”
k “Retrieve Data”
ost recent CPI value and the CPI for the same month but five years
ompute the 5 year inflation rate. Use this inflation rate to estimate
f your trip five years from now.
CPI Data Link
Enter your name in cell A2 of “Part 1 – Inflation” to
generate data.
Before wells After wells
were dug
were dug
E.Coli per ml E.Coli per ml
19
27
37
10
32
24
32
22
24
6
14
22
23
11
14
26
27
31
33
0
2
35
44
5
19
41
44
12
31
18
34
22
26
11
26
11
18
15
33
8
16
9
33
9
14
12
24
3
10
14
31
19
36
3
24
53
49
0
4
3
17
36
31
1
14
7
19
20
34
21
27
0
0
7
23
0
YOUR NAME:
From Part 1 A1
Amanda
Before
min = formula
max = formula
mean= formula
SD = formula
# of wells tested = formula
# of wells with 0 E coli = formula
Ratio
Percent Clean
Conversions
ml
29.5735
In 24 ounces
E.coli before
formula
13
33
26
44
26
14
37
31
5
18
13
10
46
25
33
16
29
35
32
39
14
26
28
23
26
17
35
32
10
29
41
30
26
25
43
30
22
27
38
27
26
2
27
22
25
30
25
17
27
34
20
23
21
20
0
18
9
0
44
11
17
16
16
14
19
32
9
26
19
0
7
10
22
18
11
35
27
18
13
14
21
27
4
31
28
15
9
0
0
17
12
11
26
29
37
3
22
15
8
14
24
19
13
15
11
11
18
30
27
23
12
33
40
28
27
36
26
20
20
28
36
38
34
16
29
24
0
14
15
0
10
21
0
11
11
1
0
10
16
18
8
12
15
31
10
12
31
10
15
1
22
31
26
16
0
18
18
0
Part 2 – Data Analysis:
Enter your name in cell A2 of “Part 1 – Infla
You have just completed a mission to Sierra
quality of water in the wells in a certain reg
well before and after your mission. You nee
for that you need to perform some statistic
from different perspectives to determine if
A2 of “Part 1 – Inflation” to
ate data.
After
min =
max =
mean=
SD =
# of wells tested =
# of wells with 0 E coli =
Before
formula
versions
formula
formula
formula
formula
formula
formula
Recall Topic 1 DQ 2
After
formula
1. Calculate descriptive statistics for your da
the statistics including mean, max and stan
there has been improvement in water quali
statistics to obtain full marks. (Fill in the be
descriptive statistics. The data has been nam
formulas.)
Answer Question 1 below:
Color Key:
oz
1
4 ounces
E. coli after
formula
formula
text/number
2. The water quality is “good” if the count o
Calculate the proportion of wells with “goo
measure does it appear that the quality of
you calculated. (In G11 and H11 calculate th
Answer Question 2 below:
3. Look at well #1 (B2 and C2) in your data.
ingest if you drank from the well before the
how many E.coli would you ingest if you dra
after the mission.)
Nothing to answer here!
ata Analysis:
r name in cell A2 of “Part 1 – Inflation” to generate data.
ust completed a mission to Sierra Leone. The goal of the mission was to improve the
water in the wells in a certain region. You collected data on the E. coli count from each
e and after your mission. You need to write a report on the success of the mission and
ou need to perform some statistical analysis on the data. You will be looking at the data
rent perspectives to determine if the water quality has improve.
e descriptive statistics for your data in the table provided in the Excel spreadsheet. Use
ics including mean, max and standard deviations of the data to decide if it appears if
been improvement in water quality? This requires a thorough discussion of these
o obtain full marks. (Fill in the before (F3:F8) and after (H3:H8) tables to the left for the
e statistics. The data has been named before and after for your convenience in creating
nswer Question 1 below:
er quality is “good” if the count of E coli is 0; otherwise, the water quality is still bad.
the proportion of wells with “good” water to wells whose water is not good. From this
does it appear that the quality of water improved? Explain and use the proportions that
ated. (In G11 and H11 calculate the percent Clean for before and after.)
nswer Question 2 below:
well #1 (B2 and C2) in your data. If you drank 24oz of water how many E.coli would you
ou drank from the well before the mission? After the mission? (In E19 and G19 calculate
E.coli would you ingest if you drank 24 oz. of water from Well 1 before the mission and
mission.)
Nothing to answer here!
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
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
63
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
39
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
78
77
88
83
70
65
74
73
79
87
79
77
66
73
85
77
53
57
68
61
32
48
52
53
58
59
57
55
52
58
63
55
Enter your name in cell A2 of
“Part 1 – Inflation” to generate data.
Before wells
were dug
E.Coli per ml
After wells
were dug
E.Coli per ml
Improvement
Data:
Before – After
19
37
32
32
24
14
23
14
27
33
2
27
10
24
22
6
22
11
26
31
0
35
44
19
44
31
34
26
26
18
33
16
33
14
24
10
31
36
24
49
4
17
31
14
19
34
27
0
5
41
12
18
22
11
11
15
8
9
9
12
3
14
19
3
53
0
3
36
1
7
20
21
0
7
All computations use
column D, the
“Improvement” data.
min = formula
max = formula
mean= formula
SD = formula
count = formula
SE = formula
Histogram – Width
Bin Width
formula
Frequency Distribution
Low
formula
formula
formula
formula
formula
formula
formula
formula
formula
formula
formula
High
Bins
formula
auto
formula
auto
formula
auto
formula
auto
formula
auto
formula
auto
formula
auto
formula
auto
formula
auto
formula
auto
formula
auto
Remember to create the Histogram.
95% Confidence Interval
Lower number
to
Higher number
formula
to
formula
23
13
33
26
44
26
14
37
31
5
18
13
10
46
25
33
16
29
35
32
39
14
26
28
23
26
17
35
32
10
29
41
30
26
25
43
30
22
27
38
27
26
2
27
22
25
0
17
27
34
20
23
21
20
0
18
9
0
44
11
17
16
16
14
19
32
9
26
19
0
7
10
22
18
11
35
27
18
13
14
21
27
4
31
28
15
9
0
0
17
12
11
30
25
37
3
22
15
8
14
24
19
13
15
11
11
18
30
27
23
12
33
40
28
27
36
26
20
20
28
36
38
34
16
29
24
26
29
0
14
15
0
10
21
0
11
11
1
0
10
16
18
8
12
15
31
10
12
31
10
15
1
22
31
26
16
0
18
18
0
Part 2 – Data Analysis:
You have just completed a mission to Sierra Leone. The goal of the mission was
wells in a certain region. You collected data on the E. coli count from a sample
mission. You need to write a report on the success of the mission and for that y
statistical analysis on the data. You will be looking at the data from different pe
water quality has improved.
Color Key:
formula
text/number
4. Since you collected water from the same source twice it makes sense to ana
well’s water quality improved. Calculate a data set that would measure the ch
each well, and the descriptive statistics for that data set, including both the s
error (SE) for the data set. (see section 3.5 of the textbook and the additional E
with this major assignment). Make a frequency distribution and histogram for
improvement in the water quality of each well in column D. (Difference in Lev
tables to the left and make a histogram of the improvement levels. (NOTE: The
is not the same as the standard error. Use the formulas from section 3.5 of the
error of the means.))
ncy Distribution
Cumulative
Frequency
formula
formula
formula
formula
formula
formula
formula
formula
formula
formula
formula
create the Histogram.
Frequency
formula
formula
formula
formula
formula
formula
formula
formula
formula
formula
formula
5. You have calculated one sample of wells and their improvement levels. If yo
wells of the, the distribution of all of those sample means would be a normal d
the 95% confidence interval of that distribution, using your sample mean as t
standard error of your sample as the population standard deviation. (Calcula
the sampling distribution in cells F30 and H30.)
6. Recall that a 95% confidence interval shows a range of values that is 95% like
your 95% confidence interval for the average improvement level is (14, 18), it w
likely to be in the range (14, 18). (See the additional Excel document provided a
Histogra
Now answer each of these questions:
a) Look at the mean for your improvement data, based on this what would you
wells.
b) Look at the confidence interval you calculated–is the value 0 inside or outsid
c) If the value 0 is outside and less than your 95% confidence interval, can you
cleaner?
d) What if the value 0 were inside your confidence interval? Could you conclud
Answer Question 6 (a):
Answer Quastion 6 (b):
Answer Question 6 (c):
Answer Question 6 (d):
eone. The goal of the mission was to improve the quality of water in
n the E. coli count from a sample of wells before and after your
ccess of the mission and for that you need to perform some
king at the data from different perspectives to determine if the
ource twice it makes sense to analyze the amount by which each
ta set that would measure the change in the number of E. coli in
hat data set, including both the standard deviation and standard
the textbook and the additional Excel document provided along
cy distribution and histogram for your data. (Calculate the
ell in column D. (Difference in Level of e. Coli.) Then, fill out the two
e improvement levels. (NOTE: The Standard deviation of this data set
e formulas from section 3.5 of the text to calculate the standard
nd their improvement levels. If you could take all possible samples of
mple means would be a normal distribution. (see section 3.5). Find
ion, using your sample mean as the population mean and the
tion standard deviation. (Calculate the 95% confidence interval of
0.)
s a range of values that is 95% likely to contain the true value of a parameter. For example, if
improvement level is (14, 18), it would mean that the true average improvement level is 95%
itional Excel document provided along with this major assignment for more details.)
ata, based on this what would you say about the change in the quality of water in the tested
ted–is the value 0 inside or outside your confidence interval?
95% confidence interval, can you conclude (with 95% confidence) that the water became
ence interval? Could you conclude (with 95% confidence) that the water became cleaner?
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
0.18
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:
88%
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: 68.37
Standard Deviation of Sampling Dist: 2.377563892
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
