Question

A random sample of size _n is taken from a normally distributed population with a population standard deviation (σ ) of 11.6. The sample mean (x) is 44.6.

Construct a 99% confidence interval about µ with a sample size of 26.

Answer 1

Given

Population Standard Devidaiton =

Sample Mena =

Sample Size = n = 26

The 99% confidence interval about µ is

Where

Since is known; So, we use Z cri.

Where

Since Confidence Interval = 99%; then Level of Significance = = 1% = 0.01

Therefore Marginal Error is

Therefore 99% confidence interval about µ is

NOTE: To See the Critical Values of Z; we use the Standard Normal area tabulated values which i posted below.

How to see?

If alpha = 1% the confidence interval = 99% Or Vice Versa

Divide the value 99 with 100. you will get 0.99 and after that divide the value 0.99 with 2; you will get 0.495. Now Search this 0.495 in side the table ( repeating again see inside the table). You will find this at the intersection of (2.5, 0,08) which is Zcri value i.e 2.58

Like this you can find the Zcri for any alpha values.