Consider a population with a known standard deviation of 143

Consider a population with a known standard deviation of 14.3. In order to compute an interval estimate of the population mean, a sample of 50 observations is drawn.

1. Compute the margin of error at a 99% confidence level. (Round your intermediate calculations to 4 decimal places. Round \"z\" value and final answer to 2 decimal places.)

2. Compute the margin of error at a 99% confidence level based on a larger sample of 200 observations.(Round your intermediate calculations to 4 decimal places. Round \"z\" value and final answer to 2 decimal places.)

Solution

(a) Given a=1-0.99=0.01, Z(0.005) = 2.58 (from standard normal table)

So the margin of error = Z*s/vn

= 2.58 * 14.3/sqrt(50)

=5.2176

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(b) So the margin of error

= Z*s/vn= 2.58 * 14.3/sqrt(200)

=2.6088