Question: Let \[{{Y}_{MAX}}\] be the sample maximum of a random sample of size 5 from a uniform distribution on the interval [0, b]. Consider the test with decision rule:

Reject b=20 in favor of b>20 when \[{{Y}_{MAX}}\ge c\]

a. Find the value of c for a 5% test.

b. Find the power of the test in part a when b = 25.

c. Assume the following data are the values of a random sample from the Y distribution:

11.74 14.59 17.71 19.42 19.71

Would the null hypothesis be accepted or rejected in this case?