Statistics please help

Can anyone help me check my work for #4? I had trouble solving #4 but made an attempt. Please advise.



3. 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?



• A level of significance of α = 0.05



n = 2 σ2 (Z (beta) + Z (alpha/2)) 2/ effect size2

z(beta) = 1.28, z(alpha) = 1.96 for two-sided test at a level of significance of 0.05

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 for a level of significance of α = 0.05 is 525.

• A level of significance of α = 0.01

n = 2 σ2 ( Z (beta) + Z (alpha/2) ) 2/ effect size2

z(beta) = 1.28, z(alpha) = 2.575 at a level of significance of 0.01

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 for a level of significance of α = 0.01 is 743.



4. 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

n = σ2 (Qe-1 + Qc-1 ) (Z(alpha) + Z(beta) 2 / μ₁²

n = 1(4) (1.645 + 1.282) 2 / (0.20)2

n = 856.7

n= 857

The required sample size for a level of significance of α = 0.05 is 857.

A level of significance of α = 0.01

n = σ2 (Qe-1 + Qc-1 ) (Z(alpha) + Z(beta) 2 / μ₁²

n = 1(4) (2.33 + 1.282) 2 / (0.20) 2

n= 1304.6

n= 1305

The required sample size for a level of significance of α = 0.01 is 1305.