# Homework Help: Statistics sample sizes

1. Jan 5, 2014

### tedpark1212

So I made an attempt to solve question 1, but I am stuck with question 2. I know that I need to use binominal distribution, but am unclear of the proper steps. Can anyone provide some help?

1. Suppose you want to show the significance of an effect size of 0.20 between your sample mean and a hypothesized mean. You intend to conduct a two-sided one-sample t-test. The sample variance is σ2 = 1.0. You assume that the population is large, or effectively infinite. If you want the test to have a power of 0.80, what is the required sample size for the following?

Attempt to solve:

• A level of significance of α = 0.05

n = 2 σ2 (Z (beta) + Z (alpa/2)) 2/ effect size2
n = 2(1) ( 1.28 + 1.96) 2/ 0.202------ for α = 0.05
n = 2 (20.9952) / 0.04
n=524.88
n= 525

The required sample size is 525 with a level of significance of α = 0.05.
• A level of significance of α = 0.01
n = 2 σ2 ( Z (beta) + Z (alpha/2) ) 2/ effect size2
n = 2(1) ( 1.28 + 2.575) 2/ 0.202------ for α = 0.01
n= 2 (14.86) / 0.04
n=743.05
n= 743
The required sample size is 743 with a level of significance of α = 0.01.

2. After some research, you determine that the size of the population is N = 350. If you want the test to have a power of 0.80, what is the required sample size for the following?

• A level of significance of α = 0.05

• A level of significance of α = 0.01

3. Comment on the sample sizes required for questions 1 and 2. Explain the differences and similarities.