1. A machine in a factory must be repaired if it produces more than 10% defectives among the large lot of items that it produces in a day. A random sample of 100 items from the day's production contains 15 defectives, and the supervisor says that the machine must be repaired.

a) Does the sample evidence support his decision? Use a test with level .01. Use the test statistic value and rejection region approach.

b) Find the p-value associated with this test.

c) According to the p-value you got in b), will we reject the null hypothesis on a 5% level? Give your reason.

d) If it is really the case that the machine produces 11% defectives among the large lot of items that it produces in a day, how likely is it that the null hypothesis of part a) will not be rejected by the level of .01 test?

e) What should the sample size be to ensure that ?

2. A machine in a factory must be repaired if it produces more than 10% defectives among the large lot of items that it produces in a day. A random sample of 20 items from the day's production contains 15 defectives, and the supervisor says that the machine must be repaired.

a) Does the sample evidence support his decision? Use a test with level .01. Use the test statistic value and rejection region approach.

b) Find the p-value associated with this test.

c) According to the p-value you got in b), will we reject the null hypothesis on a 5% level? Give your reason.

d) If it is really the case that the machine produces 20% defectives among the large lot of items that it produces in a day, how likely is it that the null hypothesis of part a) will not be rejected by the level of .01 test?

3. An experimenter was convinced that the variability in his measuring equipment results in a standard deviation of 2. Sixteen measurements yielded s2 = 6.1. Do the data disagree with his claim? Test on a 5% level.