Microorganisms play a crucial role in wastewater treatment by transforming solid organic matter into carbon dioxide and

Question:

Microorganisms play a crucial role in wastewater treatment by transforming solid organic matter into carbon dioxide and water. In a wastewater treatment system, the solids retention time is average amount of time that solid organic matter resides in the treatment tank. A study was performed at the Colorado School of Mines to determine the relationship between the solids retention time and the diversity of the microorganism population. It was thought, because microorganisms feed on the solid matter, that longer retention times would provide more opportunity for genetic mutations to occur, resulting in a greater diversity of microorganisms.
Following are counts of the numbers of species of microorganism for retention times of 3 days, 12 days, and 30 days. image text in transcribed

1. Can you conclude at the α = 0.05 level that the median number of species is greater for a retention time of 12 days than for a retention time of 3 days? Compute the appropriate test statistic, find the P-value, and state a conclusion.
2. Can you conclude at the α = 0.05 level that the median number of species is greater for a retention time of 30 days than for a retention time of 3 days? Compute the appropriate test statistic, find the P-value, and state a conclusion.
3. Can you conclude at the α = 0.05 level that the median number of species for a retention time of 30 days differs from the median for a retention time of 12 days? Compute the appropriate test statistic, find the P-value, and state a conclusion.
4. Based on the results of the tests performed in Exercises 1–3, which of the following is the best conclusion?
i. We can conclude that the median number of species increases as the solids retention time increases from 3 to 12 and from 12 to 30 days.
ii. We cannot conclude that the median number of species increases as the solids retention time increases.
iii. We can conclude that the median number of species increases as the solids retention time increases from 3 to 12 days, but it may not continue to increase as the retention time increases to 30 days.
iv. We can conclude that the median number of species increases as the solid retention time increases from 12 to 30 days, but it may not increase as the retention time increases from 3 to 12 days.