# Mathematics

## Grading Sheet

Part 1 | |||

Requirements: Answer each question fully. Use Excel formulas with cell references. Answers must be recorded on the worksheet. | |||

Possible points | Points earned | Comments | |

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 on the worksheet. | |||

Possible points | Points earned | Comments | |

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 | 0% |

## Part 1 Inflation

Input your name here | |||

name | |||

You should just use information from Major Assignment 2, but if you want to retrieve fresh CPI data, here are the instrructions again. Step 1: Go to the Bureau of Labor Statistics website at the link below. Step 2: Check U.S. All items, 1982-84=100 Step 3: Click “Retrieve Data” Use the most recent CPI value and the CPI for the same month but five years earlier to estimate the price of your trip in five years and the five year inflation rate. | |||

Month | Year | CPI | |

Unadjusted CPI, all items for 5 years ago | number | number | number |

Unadjusted CPI, all items for last month | number | number | number |

What is the 5 year inflation rate, that is percent increase in your CPI values? | formula | ||

If something cost $1.00 five years ago, what would it cost now? | formula | ||

Total budget from Worksheet 1 | number | ||

5 year projected budget total | formula | CPI Data Link | |

Like Topic 4 DQ 1 |

## Part 2 Questions 1-3

Before wells were dug – Millions of E.Coli per ml | After wells were dug – Millions of E.Coli per ml | YOUR NAME: | Joe Lope | 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. | Original Before Data | Original After Data | Random numbers | seed | ||||

23 | 52 | Before | After | 8 | ||||||||

21 | 3 | min = | formula | min = | formula | Recall Topic 1 DQ 2 | 78 | 67 | 9 | 1 | 63 | 52 |

64 | 35 | max = | formula | max = | formula | 1. Calculate descriptive statistics for your data in the table provided in the Excel spreadsheet. Use the statistics including mean, max and standard deviations of the data to decide if it appears if there has been improvement in water quality? This requires a thorough discussion of these statistics to obtain full marks. (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.) | 19 | 4 | 17 | 2 | 4 | 0 |

54 | 44 | mean= | formula | mean= | formula | 32 | 23 | 25 | 3 | 17 | 8 | |

72 | 49 | SD = | formula | SD = | formula | 125 | 110 | 33 | 4 | 110 | 95 | |

50 | 35 | # of wells tested = | formula Richard Ketchersid: Richard Ketchersid: Use =count() |
# of wells tested = | formula | 53 | 41 | 41 | 5 | 38 | 26 | |

52 | 38 | # of wells with 0 E coli = | formula Richard Ketchersid: Richard Ketchersid: Use =Countif() |
# of wells with 0 E coli = | formula | 68 | 42 | 49 | 6 | 53 | 27 | |

49 | 10 | 4 | 10 | 57 | 7 | 0 | 0 | |||||

55 | 32 | Ratio | Before | After | 106 | 79 | 65 | 8 | 91 | 64 | ||

73 | 52 | Percent Clean | formula | formula | Answer Question 1 here: | 38 | 6 | 73 | 9 | 23 | 0 | |

55 | 17 | 36 | 16 | 81 | 10 | 21 | 1 | |||||

51 | 37 | Conversions | 4 | 14 | 89 | 11 | 0 | 0 | ||||

38 | 26 | ml | oz | 17 | 5 | 97 | 12 | 2 | 0 | |||

28 | 0 | 29.5735 | 1 | 43 | 9 | 5 | 13 | 28 | 0 | |||

60 | 44 | 23 | 3 | 13 | 14 | 8 | 0 | |||||

57 | 40 | In 24 ounces | 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.) | 32 | 8 | 21 | 15 | 17 | 0 | |||

59 | 30 | E.coli before | E. coli after | 49 | 28 | 29 | 16 | 34 | 13 | |||

60 | 42 | formula | formula | 36 | 18 | 37 | 17 | 21 | 3 | |||

61 | 34 | 2 | 21 | 45 | 18 | 0 | 6 | |||||

57 | 33 | 33 | 22 | 53 | 19 | 18 | 7 | |||||

71 | 50 | 58 | 25 | 61 | 20 | 43 | 10 | |||||

57 | 40 | Answer Question 2 here: | 75 | 59 | 69 | 21 | 60 | 44 | ||||

63 | 38 | 82 | 63 | 77 | 22 | 67 | 48 | |||||

64 | 43 | 80 | 60 | 85 | 23 | 65 | 45 | |||||

63 | 52 | 70 | 52 | 93 | 24 | 55 | 37 | |||||

23 | 0 | 79 | 50 | 1 | 25 | 64 | 35 | |||||

21 | 3 | 73 | 66 | 9 | 26 | 58 | 51 | |||||

64 | 35 | 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.) | 76 | 54 | 17 | 27 | 61 | 39 | ||||

54 | 44 | 72 | 42 | 25 | 28 | 57 | 27 | |||||

72 | 49 | 72 | 55 | 33 | 29 | 57 | 40 | |||||

50 | 35 | 70 | 53 | 41 | 30 | 55 | 38 | |||||

52 | 38 | 84 | 54 | 49 | 31 | 69 | 39 | |||||

49 | 10 | Nothing to answer here! | 81 | 62 | 57 | 32 | 66 | 47 | ||||

55 | 32 | 69 | 59 | 65 | 33 | 54 | 44 | |||||

73 | 52 | 85 | 52 | 73 | 34 | 70 | 37 | |||||

55 | 17 | 100 | 69 | 81 | 35 | 85 | 54 | |||||

51 | 37 | 70 | 57 | 89 | 36 | 55 | 42 | |||||

38 | 26 | 74 | 45 | 97 | 37 | 59 | 30 | |||||

28 | 0 | 63 | 39 | 5 | 38 | 48 | 24 | |||||

60 | 44 | 76 | 60 | 13 | 39 | 61 | 45 | |||||

57 | 40 | 78 | 75 | 21 | 40 | 63 | 60 | |||||

59 | 30 | 87 | 64 | 29 | 41 | 72 | 49 | |||||

60 | 42 | 71 | 41 | 37 | 42 | 56 | 26 | |||||

61 | 34 | 83 | 67 | 45 | 43 | 68 | 52 | |||||

57 | 33 | 71 | 56 | 53 | 44 | 56 | 41 | |||||

71 | 50 | 75 | 57 | 61 | 45 | 60 | 42 | |||||

57 | 40 | 76 | 58 | 69 | 46 | 61 | 43 | |||||

63 | 38 | 63 | 39 | 77 | 47 | 48 | 24 | |||||

64 | 43 | 70 | 38 | 85 | 48 | 55 | 23 | |||||

63 | 52 | 65 | 50 | 93 | 49 | 50 | 35 | |||||

23 | 0 | 83 | 59 | 1 | 50 | 68 | 44 | |||||

21 | 3 | 76 | 48 | 9 | 51 | 61 | 33 | |||||

64 | 35 | 78 | 59 | 17 | 52 | 63 | 44 | |||||

54 | 44 | 76 | 49 | 25 | 53 | 61 | 34 | |||||

72 | 49 | 68 | 47 | 33 | 54 | 53 | 32 | |||||

50 | 35 | 77 | 51 | 41 | 55 | 62 | 36 | |||||

52 | 38 | 75 | 58 | 49 | 56 | 60 | 43 | |||||

49 | 10 | 67 | 53 | 57 | 57 | 52 | 38 | |||||

55 | 32 | 74 | 45 | 65 | 58 | 59 | 30 | |||||

73 | 52 | 86 | 58 | 73 | 59 | 71 | 43 | |||||

55 | 17 | 85 | 67 | 81 | 60 | 70 | 52 | |||||

51 | 37 | 72 | 48 | 89 | 61 | 57 | 33 | |||||

38 | 26 | 73 | 65 | 97 | 62 | 58 | 50 | |||||

28 | 0 | 59 | 43 | 5 | 63 | 44 | 28 | |||||

60 | 44 | 72 | 55 | 13 | 64 | 57 | 40 | |||||

57 | 40 | 64 | 25 | 21 | 65 | 49 | 10 | |||||

59 | 30 | 67 | 48 | 29 | 66 | 52 | 33 | |||||

60 | 42 | 79 | 55 | 37 | 67 | 64 | 40 | |||||

61 | 34 | 64 | 33 | 45 | 68 | 49 | 18 | |||||

57 | 33 | 86 | 65 | 53 | 69 | 71 | 50 | |||||

71 | 50 | 74 | 53 | 61 | 70 | 59 | 38 | |||||

57 | 40 | 83 | 61 | 69 | 71 | 68 | 46 | |||||

63 | 38 | 81 | 55 | 77 | 72 | 66 | 40 | |||||

64 | 43 | 70 | 47 | 85 | 73 | 55 | 32 | |||||

63 | 52 | 71 | 54 | 93 | 74 | 56 | 39 | |||||

23 | 0 | 68 | 54 | 1 | 75 | 53 | 39 | |||||

21 | 3 | 76 | 64 | 9 | 76 | 61 | 49 | |||||

64 | 35 | 72 | 55 | 17 | 77 | 57 | 40 | |||||

54 | 44 | 71 | 55 | 25 | 78 | 56 | 40 | |||||

72 | 49 | 86 | 77 | 33 | 79 | 71 | 62 | |||||

50 | 35 | 86 | 62 | 41 | 80 | 71 | 47 | |||||

52 | 38 | 88 | 67 | 49 | 81 | 73 | 52 | |||||

49 | 10 | 78 | 59 | 57 | 82 | 63 | 44 | |||||

55 | 32 | 73 | 45 | 65 | 83 | 58 | 30 | |||||

73 | 52 | 84 | 57 | 73 | 84 | 69 | 42 | |||||

55 | 17 | 78 | 53 | 81 | 85 | 63 | 38 | |||||

51 | 37 | 77 | 57 | 89 | 86 | 62 | 42 | |||||

38 | 26 | 88 | 68 | 97 | 87 | 73 | 53 | |||||

28 | 0 | 83 | 61 | 5 | 88 | 68 | 46 | |||||

60 | 44 | 70 | 32 | 13 | 89 | 55 | 17 | |||||

57 | 40 | 65 | 48 | 21 | 90 | 50 | 33 | |||||

59 | 30 | 74 | 52 | 29 | 91 | 59 | 37 | |||||

60 | 42 | 73 | 53 | 37 | 92 | 58 | 38 | |||||

61 | 34 | 79 | 58 | 45 | 93 | 64 | 43 | |||||

57 | 33 | 87 | 59 | 53 | 94 | 72 | 44 | |||||

71 | 50 | 79 | 57 | 61 | 95 | 64 | 42 | |||||

57 | 40 | 77 | 55 | 69 | 96 | 62 | 40 | |||||

63 | 38 | 66 | 52 | 77 | 97 | 51 | 37 | |||||

64 | 43 | 73 | 58 | 85 | 98 | 58 | 43 | |||||

63 | 52 | 85 | 63 | 93 | 99 | 70 | 48 | |||||

77 | 55 | 1 | 100 | 62 | 40 |

## Part 2 Questions 4-6

Before wells were dug – Millions of E.Coli per ml | After wells were dug – Millions of E.Coli per ml | Improvement Data: Before – After | Part 2 – Data Analysis: 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 (Q1) after your mission (Q2). 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 improved. | |||||

23 | 52 | formula | IMPROVEMENTS | |||||

21 | 3 | formula | min = | formula | All computations use column D, the “Improvement” data. | 4. Since you collected water from the same source twice it makes sense to analyze the amount by which each well’s water quality improved. Calculate a data set that would measure the improvement level of each well, and the descriptive statistics for that data set, including both the standard deviation and standard error (SE) for the data set. (see section 3.5 of the textbook). Make a frequency distribution and histogram for your data. (Calculate the improvement in the water quality of each well in column D. (Difference in Level of e. Coli.) Then, fill out the two tables to the left and make a histogram of the improvement levels. (NOTE: The Standard deviation of this data set is not the same as the standard error. Use the formulas from section 3.5 of the text to calculate the standard error of the means.)) | ||

64 | 35 | formula | max = | formula | ||||

54 | 44 | formula | mean= | formula | ||||

72 | 49 | formula | SD = | formula | ||||

50 | 35 | formula | SE = | formula | ||||

52 | 38 | formula | ||||||

49 | 10 | formula | ||||||

55 | 32 | formula | Frequency Distribution | |||||

73 | 52 | formula | Low | High | Bins | Cumulative Frequency | Frequency | |

55 | 17 | formula | Formula/Number | Formula/Number | words or formula | formula | formula | |

51 | 37 | formula | Formula/Number | Formula/Number | words or formula | formula | formula | 5. You have calculated one sample of 100 wells and their improvement levels. If you could take all possible samples of 100 wells, the distribution of all of those sample means would be a normal distribution. (see section 3.5). Find the 95% confidence interval of that distribution, using your sample mean as the population mean and the standard error of your sample as the population standard deviation. (Calculate the 95% confidence interval of the sampling distribution in cells F24 and H24.) |

38 | 26 | formula | Formula/Number | Formula/Number | words or formula | formula | formula | |

28 | 0 | formula | Formula/Number | Formula/Number | words or formula | formula | formula | |

60 | 44 | formula | Formula/Number | Formula/Number | words or formula | formula | formula | |

57 | 40 | formula | Formula/Number | Formula/Number | words or formula | formula | formula | |

59 | 30 | formula | Formula/Number | Formula/Number | words or formula | formula | formula | |

60 | 42 | formula | Formula/Number | Formula/Number | words or formula | formula | formula | 6. Recall that a 95% confidence interval shows a range of values that is 95% likely to contain the true value of a parameter. For example, if your 95% confidence interval for the average improvement level is (14, 18), it would mean that the true average improvement level is 95% likely to be in the range (14, 18). Now answer each of these questions: a) What would it mean for the average improvement in water quality to be 0? b) Look at the confidence interval you calculated–is the value 0 inside or outside your confidence interval? c) If the value 0 is outside your 95% confidence interval, can you conclude (with 95% confidence) that the water became cleaner? d) What if the value 0 were inside your confidence interval? Could you conclude in that case that the water became cleaner or not? |

61 | 34 | formula | Formula/Number | Formula/Number | words or formula | formula | formula | |

57 | 33 | formula | Formula/Number | Formula/Number | words or formula | formula | formula | |

71 | 50 | formula | Formula/Number | Formula/Number | words or formula | formula | formula | |

57 | 40 | formula | (remember to create the Histogram, too). |