The Absent-Minded Bakery sells both cream-filled and jelly-filled donuts. In the morning rush, the bakers forgot which batch was cooling on which tray and now need help in identifying the two trays.

• The weights of jelly-filled donuts follow a uniform distribution from 37 to 45 g. The mean weight of jelly-filled donuts is 41 g with a standard deviation of 2.31 g.
• The weights of cream-filled donuts follow a normal distribution with a mean of 37.5 g and a standard deviation of 1.5 g.

The bakery will set their two hypotheses as follows:

H_0

H0

: The tray contains jelly-filled donuts

H_a

Ha

: The tray contains cream-filled donuts.

We randomly select and weigh a donut from the tray. If the donut weighs 39 g or less, we'll decide that the tray it came from contains cream-filled donuts; that is we will reject H_0

H0

.

A) What is the probability of a Type I error?

This question requires a numeric input; no work is necessary. Make sure to include 4 decimal places, if appropriate and express it as X.XXXX

B) What is the power of this test?

This question requires a numeric input; no work is necessary. Make sure to include 4 decimal places, if appropriate and express it as X.XXXX

c) Suppose a Type II error is made. What type of donut is on the tray?

Jelly-filled

Cream-filled

Can't tell