Part 2:

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 (Q_{1}) after your mission (Q_{2}). 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.

- Worth 30 points. To begin with find the mean and standard deviation of each set of data. Compare the two means and standard deviations, intuitively does it appear that there has been improvement in water quality?
- Mean of Before Data =
- Mean of After Data =
- SD of Before Data =

SD of After Data =

- Worth 10 points. Pick a particular well (that has E. coli), 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?
- Amount Before Mission =
- Amount After Mission =

- Worth 20 points. Say that water quality is “good” if the count of E coli is 0. Consider 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.
- Proportion of good water wells before mission =

Proportion of good water wells after mission =

- Worth 15 points. Since you collected water from the same source twice it makes sense to consider the mean of the differences, i.e., the mean and standard deviation (SD) of the differences Q
_{1 }– Q_{2}. Find the mean of the differences and create a histogram for Q_{1 }– Q_{2}. - Worth 15 points. Find the standard deviation of the mean of the differences for Q
_{1 }– Q_{2}. Note the standard deviation of the mean of the differences is also called the standard error of the mean (SE). (See section 3.5.)- Standard deviation of differences =

Standard Error =

- Worth 10 points. Assuming that the mean of differences is normally distributed (see associated file) find the 95% confidence interval. If 0 is inside this interval what can you say? If 0 is not inside this interval, what can you say?