Do in Excel! A farmer has heard that cows produce more milk when they get to listen to classical music. He sets up an experiment to test this, where he from his 12 cows randomly selects 6 which get to listen to classical music, and 6 that do not. The resulting milk production over a week is then measured for each cow: Cow listening to classical music 113 118 126 121 111 119 no music 110 116 110 121 117 110 Use the below information: t(0.025, df=10) = 2.228, t(0.05, df=10) = 1.812, t(0.1, df=10) = 1.372, t(0.025, df=12) = 2.179, t(0.05, df=12) = 1.782 a) Farmer would like to make a hypothesis test. Assume that the observations in each group come from a normal distribution. Assume also that the population variances of two groups are the same (say, from an F-test). State hypotheses, choose a test, and carry it out with significance level 5%. How would you conclude? Do you have to make additional assumptions in order to use your test? b) Find a 90% confidence interval for the difference between the expected milk production with and without music. c) Farmer would like to study the question further, so he takes the music away from the cows that had been listening, and instead lets the other six cows listen to the music for a week. This gives him 12 new measurements. How can he analyze his new and old data together? Describe with formulas how to do the computations. Why is he likely to get a better result this time? d) Assume farmer wanted to find out whether the musical style mattered. He selects 5 different musical styles, and performs a new experiment lasting 5 weeks, where each cow gets to listen to one week of each type of music, whereafter its milk production for that week is measured. Assume farmer already knows from his past experiences that there is an individual variation from cow to cow in milk production. What kind of analysis method could he use on the resulting data? (It is enough to describe the method in one sentence.)
Do in Excel!
A farmer has heard that cows produce more milk when they get to listen to classical music. He sets up an experiment to test this, where he from his 12 cows randomly selects 6 which get to listen to classical music, and 6 that do not. The resulting milk production over a week is then measured for each cow:
| Cow listening to classical music | 113 | 118 | 126 | 121 | 111 | 119 |
| no music | 110 | 116 | 110 | 121 | 117 | 110 |
Use the below information:
t(0.025, df=10) = 2.228, t(0.05, df=10) = 1.812, t(0.1, df=10) = 1.372, t(0.025, df=12) =
2.179, t(0.05, df=12) = 1.782
a) Farmer would like to make a hypothesis test. Assume that the observations in each group come from a
with significance level 5%. How would you conclude? Do you have to make additional assumptions in order to use your test?
b) Find a 90% confidence interval for the difference between the expected milk production with and without music.
c) Farmer would like to study the question further, so he takes the music away from the cows that had been listening, and instead lets the other six cows listen to the music for a week. This gives him 12 new measurements. How can he analyze his new and old data together? Describe with formulas how to do the computations. Why is he likely to get a
better result this time?
d) Assume farmer wanted to find out whether the musical style mattered. He selects 5 different musical styles, and performs a new experiment lasting 5 weeks, where each cow gets to listen to one week of each type of music, whereafter its milk production for that week is measured. Assume farmer already knows from his past experiences that there is an
individual variation from cow to cow in milk production. What kind of analysis method could he use on the resulting data? (It is enough to describe the method in one sentence.)
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