Question

Use this formula to find a confidence interval which is xbar +/-E where E is = zc* s / sqrt n On the first one we will have a 95% confidence interval with z=1.96 and n=100 Pick a number for xbar between 60-100. Pick a number for s between 4-8. Find the confidence interval given xbar +/- E Note to find the square root of n use n^.5 where you are raising to the .5 or 1/2 power which is a square root. You can also use the square root key. Here is a short cut to use excel!!! Let's say you pick xbar = 80 and s=6. Since you have a 95% confidence interval alpha = 100%-95% =5% or .05 as a decimal n is 100. This is a z score so we use =confidence.norm(alpha, sd, n) to find E In this case you will type this in an excel cell to find E and then take the xbar + E and xbar - E =confidence.norm(.05,6,100) then hit enter If you had a t test where n< 30 then do then use the following =confidence.t(alpha,sd,n) to find E. For a proportion you will use the formula to find E. Here is an example First find phat which is p with a ^ over the p. It is equal to p/n so if p=40 and n=100 you have .4 qhat = 1- phat = .6 The confidence interval is phat +/- E where E= zc * (phat * qhat/n)^.5 So if you have a=.05 the zc = 1.96 so you have in excel for E =1.96*(.4*.6 /100)^.5 Then take (.4-E, .4+E) Go to the original problem and Instead of 100 let n=400 Show both intervals and the numbers you used. Why do you think they changed?

Answer 1

Let Zc=1.96 and n=100 ,

The 95% confidence interval is given by:

The 95% confidence interval is

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Let n=100

p=40 then phat=40/100=0.40

qhat=1-phat

=1-0.4

=0.60

Zc=1.96

The 95% confidence interval for the proportion is given by:

The 95% confidence interval for the proportion is

Let n=400

p=40 then phat=40/400=0.10

qhat=1-0.10=0.90

The 95% confidence interval for the proportion is given by:

The 95% confidence interval for the proportion is