A coin-operated coffee machine made by BIG Corporation was designed to discharge a mean of6.9

ounces of coffee per cup. If it dispenses more than that on average, the corporation may lose money, and if it dispenses less, the customers may complain. Believing that the mean amount of coffee

dispensed by the machine is less than6.9

ounces,BIG plans to do statistical test of the claim that the machine is working as designed. BIG gathers a random sample of100

amounts of coffee dispensed by the machine.

Suppose that the population of amounts of coffee dispensed by the machine has a standard deviation of

0.8

ounces and that BIG performs its hypothesis test using the0.1

level of significance.Based on this information, answer the questions below. Carry your intermediate computations to at least four decimal places, and round your responses as indicated.

(If necessary, consult alist of formulas.)

What are the null and alternative hypotheses that BIG should use for the test?H

0

:

is

?

less than

less than or equal to

greater than

greater than or equal to

not equal to

equal to

?

0.8

6.70

6.9

100

H

1

:

is

?

less than

less than or equal to

greater than

greater than or equal to

not equal to

equal to

?

0.8

6.70

6.9

100

What is the probability that BIG commits a Type I error? Round your response to at least two decimal places.

Assuming that the actual value of is 6.70 ounces, what is the probability that BIG commits a Type II error? Round your response to at least two decimal places.

Suppose that BIG decides to perform another statistical test using the same population, the same null and alternative hypotheses, and the same level of significance, but for this second test BIG chooses a random sample of size 150 instead of a random sample of size 100. Assuming that the actual value of is 6.70 ounces, how does the power of this second test compare to the power of the original test?

The power of the second test is greater than the power of the original test

The power of the second test is less than the power of the original test

The powers of the two tests are equal