Question

x= 50 n=12 sigma o= 6 confidence =99%

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(a/2) x o/ square root of n

Identify the critical value.

What is the margin of error obtained using the methods of parts​ (b) and​ (c)?

Answer 1

a) The population standard deviation is known hence Z distribution is applicable

The formula for estimation is:

μ = M ± Z(s_M)

where:

M = sample mean
Z = Z statistic determined by confidence level
s_M = standard error = √(s²/n)

M = 50
Z = 2.58
s_M = √(6²/12) = 1.73

μ = M ± Z(s_M)
μ = 50 ± 2.58*1.73
μ = 50 ± 4.46

99% CI [45.54, 54.46].

b) Using Confidence interval the margin of error is calculated as

(45.54+54.46)/2 =100/2=50 and Margin of error= 50-45.54=4.46

c) Using formula as well

Z(s_M)

=2.58*√(6²/12)

=4.46

The crirtical value is calculated using Z tabl;e shown below as

= 2.58 at 99 5 confidnece level