A simple random sample of size n is drawn. The sample mean, x, is found to be 17

ID: 3428732 • Letter: A

Question

A simple random sample of size n is drawn. The sample mean, x, is found to be 17.9, and the sample standard deviation, s, is found to be 4.7.

a) Construct a 95% confidence interval about u if the sample size, n, is 34.

The confidence interval is_

(use ascending order. Round to two decimal places as needed.)

b) Consruct a 95% confidence interval about u if the sample size, n, is 61

The confidence interval is_

(Use ascending order. Round to two decimal places as needed.)

How does increasing the sample size affect the margin of error, E? (choose a,b or c)

a)The margin of error increases

b)The margin of error does not change

c) The margin of error decreases.

(a) Given a=0.05, Z(0.025) = 1.96 (from standard normal table)

So the lower bound is

xbar - Z*s/vn = 17.9 -1.96*4.7/sqrt(34) = 16.32

So the upper bound is

xbar + Z*s/vn = 17.9 +1.96*4.7/sqrt(34) =19.48

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(b)

So the lower bound is

xbar - Z*s/vn = 17.9 -1.96*4.7/sqrt(61) = 16.72

So the upper bound is

xbar + Z*s/vn = 17.9 +1.96*4.7/sqrt(61) =19.08

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