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