Question

Why are there 2 equations to determine a sample size of a proportion?

Explain How are confidence intervals interpreted?

List the 4 confidence levels and their corresponding Z score.

Why do population means require the use of the T score?

Answer 1

1) If historical value for proportion known:

If we have given then we can use following formula.

i.e.   given or historical value known for p

if historical value for is not known then use

Formula is

2) For example: If repeated samples are drawn and 99%confidence interval calculated for each sample we are 99% confident that 99% interval would contain population mean(i.e. Population parameter value)

3)

Confidence level	Z value
90%	1.645
95%	1.96
98%	2.33
99%	2.58

4) When sample size less than 30 and population standard deviation are unknown then use confidence interval by t

We can use here formula.