Reference no: EM132856576

Question:

1. First we'll see if the test has the correct size. Obviously, we can't actually conduct an experiment. Also, conducting the experiment once won't tell us if the size is actually close to . We can, however, simulate some results under the assumption that is true. If we conduct a similar, simple experiment that can be carried out many times in the lab, we can get an idea of the size of the test in practice. The experiment is carried out for (the null hypothesis) many times, the proportion of times we can reject the null hypothesis is the estimated size of the test. We will be carrying out the small experiment 20 times.

a. If is true, how many times should you expect to reject?

b. Each group should have two n-sided dice (where n=4, 6, 8, 10, 12, or 20). Roll one die twenty times. If the result is 1 to n/2 count this as a success (for example, if n=4, then 1 to 2 would be counted as success or if n=12, then 1 to 6 would be counted as success). If the result is greater than n/2 count this as a failure (this gives P(success)=P(failure)=0.50). Based on the twenty trials (which represent the twenty calves), what is the decision? Repeat the experiment 19 more times (i.e. carry out a total of 20 tests of :). A tabulation sheet is provided (p. 4), and the extra die is so that different group members can be carrying tests simultaneously to save time.

i. How many times out of 20 did you reject?

ii. What is the estimated size of the test (proportion of times you reject the null hypothesis)?

iii. Should the physiologist be satisfied that the test has size close to the specified?

c. Each group will be assigned a specific alternative value. Your group's alternative value is π=0.3 . Using the binomial table, find the power of the test under your group's alternative.

i. The power is:

ii. This power means that out of 20 tests, we should expect to reject how many times under this alternative?