Question

1.

A. According to Fidelity Investments, through last month, the majority of companies reporting profits had beaten estimates. A sample of 160 companies showed that 96 beat estimates, 38 matched estimates, and 26 fell short of estimates. Using this information, how large a sample is needed to estimate the true proportion of all companies that had beaten estimates if you want to be 97% certain of being within 2% of the true proportion?

Answer: n =

B.

Customers arrive at a movie theater at the advertised movie time only to find that they have to sit through several previews ads before the movie starts. Many complain that the time devoted to previews is too long. A preliminary sample conducted by the local newspaper showed that the standard deviation of the amount of time devoted to previews was 3 minutes. Use that as a planning value for the standard deviation. If we want to estimate the population mean time for previews at movie theaters with 96% confidence, with a margin of error of 75 seconds, what sample size should be used?

Answer:  n =

Answer 1

Solution: 1. A. The proportion of all companies that had beaten estimates is A96 160 = 0.6 Then, 0 0.6(1-0.6) 2 0.02 (Zoous) 0.24 015 0.0004 (2.17)2 0.24「Fromthestandard normal 0.0004 - 2, 825.34 2, 825 probabilities table

From the given information, the population standard deviation is 3 minutes Then, σ 3x60 -180seconds The sample size is Zoo4 | 1802 75 (Zoo" (32.400) 5,625 (2.05) (32,400) From thestandardnormal 5,625 probabilitiestable = 24.2064 24