A simple random sample of size n is drawn. The sample mean, x, is found to be 18

Question

A simple random sample of size n is drawn. The sample mean, x, is found to be 18 9. and the sample standard deviation, s, is found to be 4.3. Construct a 95% confidence interval about mu if the sample size, n, is 34. Lower bound:: Upper bound: (Use ascending order. Round to two decimal places as needed.) Construct a 95% confidence interval about mu if the sample size, n, is 51. Lower bound:: Upper bound: (Use ascending order. Round to two decimal places as needed.) How does increasing the sample size affect the margin of error, E? A. The margin of error increases. B. The margin of error does not change C. The margin of error decreases Construct a 99% confidence interval about mu if the sample size, n, is 34 Lower bound:: Upper bound: (Use ascending order. Round to two decimal places as needed.)

Explanation / Answer

a)

margin of error = 1.96 * 4.3/sqrt(34)

= 1.445

lower bound = 18.9 - 1.445 = 17.46

upper bound = 18.9 + 1.445 = 20.25

b)

margin of error = 1.96 * 4.3/sqrt(51)

= 1.18

lower bound = 18.9 - 1.18 = 17.72

upper bound = 18.9 + 1.18 = 20.08

c)

margin of error decreases

d)

margin of error = 2.575 * 4.3/sqrt(34)

= 1.899

lower bound = 18.9 - 1.889 = 17.01

upper bound = 18.9 + 1.889 = 20.79

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