In a test environment, a particular dehumidifier is designed to remove over 55 quarts of water in a 24-hour period. To look for support of this performance, a research team plans to record the amount of water removed for a sample of 12 days; the dehumidifier will be reset after each use. (a) What are the null and alternative hypotheses appropriate for the research team? Define any parameter(s) used.
(b) How high must the average amount of water removed be in this sample in order to conclude that the dehumidifier is performing correctly, assuming a significance level of .05? Past research has shown that the standard deviation for such dehumidifiers is 5 quarts. You may also assume that observations are approximately normally distributed.
(c) After the study is over, it turns out that the average is 57 quarts removed for the 12 days with standard deviation 6.1. Calculate the test statistic for this test, and state the conclusion at the .05 level.