Exercises. 1. Perform the following tests of hypothesis assuming that the population of paired differences are normally distributed.

1. Perform the following tests of hypothesis assuming that the population of paired differences are normally distributed.

a) ; ; ; ; ;

b) ; ; ; ; ;

c) ; ; ; ; ;

2. It is claimed that an industrial safety program is effective in reducing the loss of working hours due to factory accidents. The following data are collected concerning the weekly hours due to accidents in nine plants both before and after the safety program is installed

Before
After

Do the data substantiate the claim? Use .

Assume that the population of paired differences is (approximately) normally distributed.

3. A company claims that the course it offers significantly increases the writing speed of secretaries. The following table gives the scores of 8 secretaries before and after they attended this course

Before
After

Using the 5% significance level, can you conclude that attending this course increases the writing speed of secretaries?

Assume that the population of paired differences is (approximately) normally distributed.

4. A random sample of nine employees was selected to test for the effectiveness of hypnosis on their job performance. The following table gives the job performance ratings (on a scale of 1 to 4, with 1 being the lowest and 4 being the highest) before and after these employees tried hypnosis.

Before	2.3	2.8	3.1	2.7	3.4	2.6	2.8	2.5
After	2.6	3.2	3.0	3.5	3.7	2.4	2.9	2.9

Test at the 5% significance level if there is an improvement in the job performances of employees due to hypnosis.

Assume that the population of paired differences is (approximately) normally distributed.

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