Statistics question
One can calculate the 95% confidence interval for the mean with the
population standard deviation known. This will give us an upper and a lower
confidence limit. What happens if we decide to calculate the 99% confidence
interval? Describe how the increase in the confidence level has changed the
width of the confidence interval. Do the same for the confidence interval set at
90%. Do an example and give real values for the intervals in your post.
The formula for a confidence interval is:
x̄ +/-
zα/2
∙σ/
sqrt(n)
Use that formula with the numbers plugged into it.
x̄ is the sample mean and n is the sample size (no. of samples collected).
The population standard deviation is denoted by the greek letter sigma
σ:
(1-α)*100% is the level of
confidence.
For example, in a 95% confidence interval
1- α =.95 Solving for α
gives
α =.05(Also, see Table 8.1 on
page 359, under 95% confidence). Thus:
α/2 = .05/2 =.025zα/2 denotes the z
value on the bell-shaped curve whose right-tail area is α/2 .
For example, on page
292 (under “what is this z value?”), the z value there is denoted by z.10 since
the right-tail area of that z value is .10.
If you are doing a 95% confidence interval for the mean using formula 8.1 on
page 358, then
zα/2
= z.025
= 1.96
by looking up the z-value on table 8.1 on page 359 (under confidence level
95%). This means that the area to the right of z=1.96 is .025.
