Question

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version 3 Questions 16 - 18 A survey of 100 businesses revealed that the mean after-tax profit was $80,000 and the standard deviation was $12,000. You would like to formally estimate the population mean after-tax profit of a business. Q16 Suppose that you use the sample mean as the estimator. Find the standard error of the estimator. (a) 80,000 (b) 12,000 (c) 1,200 (d) 120 (e) 800 Answer (c) 1200 Q17 Find the 95% confidence interval for the population mean. (a) (76904, 830961 (b) 77204, 82796 (e) (77648, 823521 (d) (78032, 81968 (e) 178464, 81536 Answer (c) Q18 You want to improve precision of the interval estimator by making the margin of error as low as 1,500 at the confidence level of 99%. What is the minimum required sample size for this level of precision? (a) 427 (b) 317 (c) 246 (a) 173 (e) 105 Answer (a)

Answer 1

Q 16) The correct answer is option C

Standard error of the estimator =

Standard error of the estimator = 12,000 V100

Standard error of the estimator og = 1200

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Q 17) The correct answer is option C

The 95% confidence interval is given as

X2 = X-Zox & X2 = X + Z ox

The Z score for 95% confidence interval = 1.96

X4 = 80,000 - 1.96 x 1200 & X2 = 80,000 + 1.96 X 1200

X₁ = 77,648 & X₂ = 82,352

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Q 18) The correct answer is option a

The sample size is given as

2202 n = E2

For a confidence level of 99%, the Z score = 2.58

n =- 2.582 x 120002 15002

Sample size n $\approx$ 427