According to Thomson Financial, last year the majority of companies reporting profits had beaten estimates. A sample of 162 companies showed that 102 beat estimates, 29 matched estimates, and 31 fell short. (a)What is the point estimate of the proportion that fell short of estimates? If required, round your answer to four decimal places. pshort = (b)Determine the margin of error and provide a 95% confidence interval for the proportion that beat estimates. If required, round your answer to four decimal places. ME = (c)How large a sample is needed if the desired margin of error is 0.05? If required, round your answer to the next integer. n* =

a) Given that, n = 162 x = 31 Point estimate = sample proportion = short = x / n = 31/162 = 0.1914 1 - short = 0.8086 b) Solution : Given that, n = 162 x = 102 Point estimate = sample proportion = = x / n = 102/162 = 0.6296 1 - = 0.3704 At 95% confidence level the z is , = 1 - 95% = 1 - 0.95 = 0.05 / 2 = 0.05 / 2 = 0.025 Z/2 = Z 0.025 = 1.96 Z/2 = 1.96 Margin of error = E = Z / 2 * (( * (1 - )) / n) = 1.96 * ((0.6296*0.3704) / 162) = 0.0744 A 95% confidence interval for population proportion p is , - E < p < + E 0.6296 - 0.0744 < p < 0.6296 + 0.0744 0.5552 < p < 0.7040 The 95% confidence interval for the population proportion p is : 0.5552 < p < 0.7040c) Solution : Given that, = 0.6296 1 - = 0.3704 margin of error = E = 0.05 At 95% confidence level the z is , = 1 - 95% = 1 - 0.95 = 0.05 / 2 = 0.05 / 2 = 0.025 Z/2 = Z 0.025 = 1.96 sample size = n = (Z / 2 / E )2 * * (1 - ) = (1.96 / 0.05)2 * 0.6296*0.3704 = 358.3503 sample size = 359

Answered: According to Thomson Financial, last…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

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According to Thomson Financial, last year the majority of companies reporting profits had beaten estimates. A sample of 162 companies showed that 102 beat estimates, 29 matched estimates, and 31 fell short.

(a)	What is the point estimate of the proportion that fell short of estimates? If required, round your answer to four decimal places.
	p_short =
(b)	Determine the margin of error and provide a 95% confidence interval for the proportion that beat estimates. If required, round your answer to four decimal places.
	ME =
(c)	How large a sample is needed if the desired margin of error is 0.05? If required, round your answer to the next integer.
	n^* =

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