1.According to Thomson Financial, through January 25, 2006, the majority of companies reporting profits had beaten estimates (BusinessWeek, February 6, 2006). A sample of 162 companies showed 104 beat estimates, 29 matched estimates, and 29 fell short.
a. What is the point estimate of the proportion that fell short of estimates?
b. Determine the margin of error and provide a 95% confidence interval for the proportion that beat estimates.
c. How large a sample is needed if the desired margin of error is .05?
2. The percentage of people not covered by health care insurance in 2003 was 15.6% (Statistical Abstract of the United States, 2006). A congressional committee has been charged with conducting a sample survey to obtain more current information.
a. What sample size would you recommend if the committee's goal is to estimate the current proportion of individuals without health care insurance with a margin of error of .03? Use a 95% confidence level.
b. Repeat part (a) using a 99% confidence level.