Question

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)

____

Answer 1

A)

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

B)

Margin of error = Width of CI / 2

= (57.44 - 50.56 ) / 2

= 3.44

C)

E = 2.576 * 5 / sqrt(14)

= 3.442