Students and professors in the Nursing and Engineering Departments at Hope College went to the cen- tral African country of Cameroon to help improve drinking water quality and community health in rural communities by installing water filters in or near homes in one village. The families living in this village had no electricity, had no water distribution system, and got their water from streams. The filters they installed contained a diffuser plate, fine sand, coarse sand, and gravel. Using the new filters, family mem- bers were expected to gather their water and filter it before drinking, instead of drinking directly from the stream as was common practice.

Students working on this project examined the quality of the filters by looking at many different variables, including general observations, filter observations, microbiology observations, household prac- tice observations, user perceptions, and water source observations. It should be noted, when making inferences, the water filters in this dataset should be treated as a sample of all filters that could be con- structed if this pilot project were expanded to other villages. Thus, inference is to an as-yet-unbuilt, larger population of filters.

data:

ecoli time:

day 1: day 2:

18 193

200 193

77 137

4 62

170 246

5 9

0 0

6.7 17

33 27

50 162

10 102

0 12

2 132

33 35

ecoli sand:

sand_level

day_1

above 18

above 0

below 200

above 77

above 4

below 170

above 263

above 75

above 5

above 0

below 0

above 6.7

above 33

above 50

above 10

below 0

above 0

above 2

below 33

4.Are the samples of the firstE.colicount independent or dependent of the samples of the secondE.colicount? Explain. Based on your answer, is this an independent samples or paired design?

6.State the null and alternative hypotheses to be investigated with this study in symbols or in words.

9.Carry out an appropriate test of significance to see whether, on average, there is a genuine difference between the firstE. colicount and the secondE. colicount. Report your p-value and a 95% confidence interval.

10.Based on your p-value and confidence interval, what conclusions can you draw from this test?

15.Are the samples of the firstE. colicount independent or dependent of the samples of the secondE. colicount? Explain.

17.Carry out an appropriate test of significance to see whether on average there is a difference in theE. colicounts between filters with more than 2 inches of sand and those with less. Report your p-value, a 95% confidence interval, and your conclusion.