The U.S. Department of Labor wants to estimate the percentage of females in the labor force to within ±2% with 90% confidence. As a planning value they use 46%, the reported percentage of females in the labor force of EU (European Union) countries. How many employment records should be sampled?

A 382

B 121

C 1681

D 269

E 451

EU (European Union) countries report that 46% of their labor force is female. The United Nations wants to determine if the percentage of females in the U.S. labor force is the same. Representatives from the United States Department of Labor select a random sample of 525 from over 10,000 employment records on file and find that 229 are female. The 90% confidence interval for the proportion of females in the U.S. labor force is

A 0.2747 to 0.5973

B 0.4235 to 0.5679

C 0.3998 to 0.4722

D 0.1243 to 0.7100

E 0.1776 to 0.6944

A large software development firm recently relocated its facilities. Top management is interested in fostering good relations with their new local community and has encouraged their professional employees to engage in local service activities. They believe that the firm’s professionals volunteer an average of more than 15 hours per month. If this is not the case, they will institute an incentive program to increase community involvement. A random sample of 24 professionals yields a mean of 16.6 hours and a standard deviation of 2.22 hours. The P-value associated with the resulting test statistic is 0.0009. At a = 0.05, which of the following is the correct conclusion?

I. We reject the null hypothesis.

II. We fail to reject the null hypothesis.

III. The firm shouldn’t need to institute an incentive program because the evidence indicates that professional employees volunteer an average of more than 15 hours per month in their local community.

A I only

B II only

C II and III only

D I and III only

E III only