Documents
Resources
Learning Center
Upload
Plans & pricing Sign in
Sign Out

Lab 8

VIEWS: 0 PAGES: 2

									                                   Lab 8
                              STA 570 401-404
                           Sample Size calculations
Objectives : To practice computing sample sizes required to achieve particular
experimental design criteria, such as type I and power values.

To start : Log in to the computers and start Word. We will not be using SAS for this lab.

Remember the formula from lecture for sample size determinations
                               2
    z1s1  z0 s0 
n               
    p0  p1 
With your TA

   1) Suppose we wish to test H0 : p=0.4 against H1 : p>0.4 using α=0.01. We also wish
      to achieve 80% power when p=0.42. What is the minimal required sample size?
      Here we have a “greater than” alternative, so we need to equate the 1-α=0.99
      percentile of the null distribution to the 1-POW=0.20 percentile of the alternative
      distribution. Thus, z0=2.33, z1=(-0.84), s0=sqrt(0.4*0.6)=0.4899, and
      s1=sqrt(0.42*0.58)=0.4936. The required sample size is

            ( 084)(0.4936)  (2.33)(0.4899) 
                                                                      2
                 .
        n                                     6053548
                                                      .
                       0.4  0.42            

   2) Suppose we wish to test H0 : p=0.3 against H1 : p≠0.3. We wish to use α=0.05 and
      achieve 90% power with p=0.35. What is the minimal required sample size? Here
      will have a “not equal” alternative with a p1 greater than p0. Thus we need to
      equate the 1-(α/2)=0.975 percentile of the null distribution to the 1-POW=0.10
      percentile of the alternative distribution. Thus z0=1.96, z1=(-1.28),
      s0=sqrt(0.3*0.7)=0.4583, and s1=sqrt(0.35*0.65)=0.4770. Thus the minimal
      required sample size is

            ( 128)(0.4770)  (196)(0.4583) 
                                                                       2
                 .               .
        n                                    910.625
                       0.3  0.35           
On your own

   1) You are testing a roulette wheel. In theory, the roulette wheel should produce
      18/38 (0.4737) black spins. You want to test whether or not the wheel actually
      produces this probability (erring on either side is bad). You want to use α=0.10
      and want to achieve 99% power when p=0.45. What is the minimal required
      sample size?
   2) You want to test whether a counseling program for married couples reduces the
      divorce rate below 30%. You will enroll n couples in the program and observe
      how many still get divorced. You want to have the type I error probability equal
      to 0.05 and achieve 90% power if the program reduces the divorce rate to 25%.
      What is the minimal number of couples required?

								
To top