MGMT2263 Tutorial Sheet #2

1) The average weekly wage for a sample of 30 employees in Firm A is $480 with a standard deviation of $14. In Firm B, a random sample of 40 employees has an average weekly wage of $470 with a standard deviation of $10. Based on these samples, is there any significant difference in the average weekly wages of the 2 companies? Test at a 5% level of significance. (Z = 3.3272; conclude the average weekly wages are not the same)

2) Is there any level of significance between 1% and 10% in which you would have changed the verdict in question 1? (p-value = 0.0008; no)

3) Construct a 95% confidence interval of the difference of the average weekly wage. Why would you reach the same conclusion as in question 1? ($4.11 < m_A - m_B < $15.89; we would reject Ho since the hypothesized difference of m_A - m_B = 0 does not fall in the confidence interval)

4) Suppose that in question 1, the sample sizes and standard deviations remained the same but the sample means were different. What would be the largest difference between the sample means in which Ho would not be rejected if a 5% level of significance were used? ($5.89)

5) A hardware manufacturer created a new communications device to rival the Blackberry but meant to be used by both working professionals and the general public. However, it suspected the average difference between the number of hours per month that working professionals would use it and ordinary people would exceed 50 hours per month. For samples of 400 from each group these were the statistics:

	Professionals	General public
mean	240	180
standard deviation	65	45

Do not assume a level of significance. (Z = 2.53; p-value = 0.0057; Conclude the average difference between professionals and the general public is more than 50 hours per month)