A sample mean, sample size, population standard deviation, and confidence level are provided. Use this information to complete parts (a) through (c) below.
x=54, n=14, σ=5, confidence level=99%
A. Use the one-mean z-interval procedure to find a confidence interval for the mean of the population from which the sample was drawn.
The confidence interval is from ___to___
B. Obtain the margin of error by taking half the length of the confidence interval.
What is the length of the confidence interval? ____
C. Obtain the margin of error by using the formula E=z α/2 • σ/square root n.
Identify the critical value.
z α/2 =____
What is the margin of error obtained using the methods of parts (b) and (c)
99% confidence interval for is
- z * / sqrt(n) < < + z * / sqrt(n)
54 - 2.576 * 5 / sqrt(14) < < 54 + 2.576 * 5 / sqrt(14)
50.56 < < 57.44
The confidence interval from 5056 to 57.44
Margin of error = Width of CI / 2
= (57.44 - 50.56 ) / 2
E = 2.576 * 5 / sqrt(14)
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