A dairy farmer has heard that cows produce more milk when th

A dairy farmer has heard that cows produce more milk when they listen to
classical music. He sets up an experiment to test this, where he randomly selects 6 cows
that get to listen to classical music and 6 other cows that do not. The resulting milk
production over a week is then measured for each cow. The results are summarized in the
following table:

(a) Conduct an appropriate statistical test: define H0 and Ha, the test statistic, and the
rejection region. Clearly state the assumptions that need to be made for your test. Provide
the ANOVA table, report the corresponding p-value for the test, and give your conclusion
regarding the effect of classical music on cows’ milk production.

(b) Find a 90% confidence interval for the difference between the expected milk
production with and without music. Does it suggest a conclusion consistent with part (a)?

Cows listening to classical music 113118 126 121 111119 Cows with no music 110 116 110 121 117110

Solution