Question:

Performing and conducting test hypothesis on two independent samples

Solve the following as indicated. Show the steps in hypothesis testing.

1.Two processes in a manufacturing line are performed manually: operation A and operation B. A random sample of 45 different assemblies using operation A shows that the sample average time per assembly is 8.5 minutes, with a population standard deviation of 1.30 minutes. A random sample of 40 different assemblies using operation B shows that the sample average time per assembly is 7.4 minutes, with a population standard deviation of 1.20 minutes. Using 5% level of significance, is there enough reason to believe that operation A takes significantly longer to perform than operation B?

2. New employees at ECP Company are required to attend a three-day seminar to learn about the company. At the end of the seminar they are tested to measure their knowledge about the company. The traditional training method has been lecture and a question-and-answer session. Management decided to experiment with a different training procedure, which processes new employees in two days by using videocassettes with no question-and-answer. If this procedure works, it could save the company millions of pesos over a period of several years. To test the difference in the two methods, the managers randomly select one group of 16 newly hired employees to take the three-day seminar (Method A) and a second group of 12 new employees for the two-day videocassette method (Method B). The table below shows the test scores.

Training Method A	Training Method B
56 50 53 45 52 47 45 48 53 44 43 51 47 53 48 43	59 64 56 57 55 54 56 67 52 56 57 52

Using 5 % level of significance, test if there is a significant difference in the mean scores of the two groups.

3.A large production facility uses two machines to produce a key part for its main product. Inspectors have expressed concern about the quality of the finished product. Quality control investigation has revealed that the key part made by the two machines is defective at times. The inspectors randomly sampled 40 units of the key part from each machine. Of those produced by machine A, five were defective. Seven of the 40 sampled parts from machine B were defective. Using 1% level of significance, can the investigators conclude that the proportion of defective parts coming from machine B is significantly higher than that of machine A?

Performing and conducting test hypothesis on two dependent samples

Solve the following as indicated. Show the steps in hypothesis testing.

4. Ten employees were put under the care of the company nurse because of high cholesterol readings. The nurse lectured them on the dangers of this condition and put them on a new diet. Shown are the cholesterol readings of the ten employees both before the new diet and one month after use of the diet began.

Employee	Before	After
1 2 3 4 5 6 7 8 9 10	236 219 225 230 215 250 300 242 290 230	223 203 200 240 190 235 240 215 215 225

At 5% level of significance, can you conclude that the new diet is effective in reducing the cholesterol levels?