# Statistics - Hypothesis Testing

1. A manufacturing firm recruits 45 new sales staff, and sends each on one of two training courses. 25 attend course A, and 20 attend course B. The sales figures are then collected for the following six months and the following summary statistics are produced from profits X (in pounds) generated from these sales:

(see attached file for formulas)

The firm's manager decides to analyse the data using a two sample t-test. What assumptions is she making? Write down the distributions of X1, X2 which following from these assumptions, and, by combining these two training courses generate equal mean profits.

9. Using the t-distribution with the appropriate value for the degrees of freedom, show that the null hypothesis of equal mean profits in QS can be rejected at the 10 percent significance level, but accepted at the 3 percent significance level. Without calculating the precise value, give an approximate estimate of the p-value for this hypothesis. What advice on future training of new sales staff would you give to the manager?

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#### Solution Preview

Please also see attached Excel file.

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(8) The assumption made in this hypothesis test is that the distributions of the sales figures for students from both the training courses follow a normal distribution.

H0: The mean profits generated from both the courses are equal, that ...

#### Solution Summary

Complete step-by-step calculations for problems involving profit distribution and hypothesis testing.