Q.1 Paired

A manager of a t-shirt company wants to analyse an efficiency training program that was recently implemented in her manufacturing department. She wishes to test whether there has been an improvement in the quantity of t-shirts produced as a result of the training.

The manager randomly selects 9 employees at the beginning of a training session and records the individual numbers of t-shirts they produced in one week. At the end of the training, the same employees have their productivity recorded again. The following data was collected:

Weekly Number of T-shirts Produced

Employee	Before training	After training
1	111.5	115
2	120	124
3	131	132
4	134	137
5	135	135
6	142	144
7	142	142
8	146	146
9	140	140

Test the following Null and alternative hypotheses:

H_o: D 0

H₁: D < 0 where D is Before - After

Also consider alpha of 0.01 for this test.

a) What is the sample mean of the differences?

b) What is the sample standard deviation of the differences? (use two decimal places)

c) What is the Decision Rule? (e.g. Reject the null if the test stat is < or > ???)

d) What is the Test Statistic?

e) What is the conclusion?

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