You may need to use the appropriate technology to answer this question.

According to Thomson Financial, last year the majority of companies reporting profits had beaten estimates. A sample of 158 companies showed that 105 beat estimates, 25 matched estimates, and 28 fell short.

(a)

What is the point estimate of the proportion that fell short of estimates? (Round your answer to four decimal places.)

p =

(b)

At 95% confidence, determine the margin of error for the proportion that beat estimates. (Round your answer to four decimal places.)

Provide a 95% confidence interval for the proportion that beat estimates. (Round your answers to four decimal places.)

to

(c)

How large a sample is needed if the desired margin of error is 0.05? (Round your answer up to the next integer.)