Part 2. Finding Confidence Interval for Population Mean based on sample data.

Write a ny 5-8 numbers between 1 and 40. They will represent sample data.

Calculate Sample Mean (x) and Sample Standard Deviation (s).

Based on this sample data we will predict population mean. Not exact value,

but interval that holds population mean, so called Confidence Interval:

Confidence Interval:x Eor (x- E,x+ E)

werexis calculated sample mean andE is a Margin of Error.

In the case when we have sample standard deviation (s)

but population standard deviation () is unknown,

we calculate Margin of Error by formula:

E = t_a/2 s/n

n - sample size,

t_a/2is not t_adivided by 2, it's just t-value from theAppendix Table for t-Distribution.

To find t-value from the Table we use row with Degree of Freedom df=n-1

and columns forArea in Two Tails.

What column to use: 0.01, 0.02, 0.05, 0.10 or 0.20?

It depends on the given Confidence Level.

For example, if given Confidence Level is 90% , convert it in decimal form: 0.90,

then calculate 1 - Conf.Level = 1 - 0.90 = 0.10. That's the column you should use.

(1 - Conf.Level) is called Significant Level. Sometimes, instead of Confidence Level

Significant Level is given and we know right away what column to use.

Here are steps to follow:

1) Write 5-8 numbers between 1 and 40; this will be your sample data.

2) Calculate sample mean (x) and sample standard deviation (s).

3) UseAppendix Table for t-Distributionto find t-value.

4) Calculate Margin of Error (E) using theformula above.

5) Write Confidence Interval for Population Mean:=x E or (x E, x + E)