1. Before the hiring of an efficiency expert, the mean productivity of a firm's employees was 45.4 units per hour, with a standard deviation of 4.5 units per hour. After incorporating the changes recommended by the expert, it was found that a sample of 30 workers produced a mean of 47.5 units per hour. Using the 0.01 level of significance, can we conclude that the mean productivity has increased?

2. The average U.S. family includes 3.13 persons. To determine whether families in her city tend to be rep- resentative in size compared to those across the United States, a city council member selects a simple random sample of 40 families. She finds the average number of persons in a family to be 3.40, with a standard deviation of 1.10. Source: Bureau of the Census, Statistical Abstract of the United States 2009, p. 52.

a. Using a nondirectional hypothesis test and a level of significance of your choice, what conclusion would be reached?

b. For the significance level used in part (a), construct the appropriate confidence interval and verify the conclusion reached in part (a).