Environmental engineers have found that the percentages of active bacteria in sewage specimens collected at a sewage treatment plant have a non-normal distribution with a median of 40% when the plant is running properly. If the median is larger than 40%, some adjustments must be made. The percentages of active bacteria (PAB) in a random sample of 10 specimens are saved in the t3e8 Excel file. Do the data provide enough evidence (at a = 0.05) to indicate that adjustments are needed?

a) What are the null and alternative hypotheses?

b) Which test(s) can be used to answer this question? What are the required conditions? Do you think that these conditions are likely satisfied this time? Explain your answer.

c) Perform the test(s) first manually and then with R. Explain your decision and conclusion.