Question

Exercises 10.3. Let Xi . . . , x N μ, σ2), whereơ2 s known to be equal to 100. In testing Ho : 25vs. H :H>25,h What sample size n would be necessary if one wishes to reject Ho with probability at least 95 if μ 26? iid se that a coin is to be tossed n times, and you wish to test the hypothesis Ho:p-12 VS. Hi P> I/2 at a- .05. What sample size n would be necessary if you want to reject Ho with probability 90 if p 55? Since the sample size will be reasonably large in this roblem, the approximate normality of the sample proportion p may be assumed. oin is to be tossed n times, and you wish to test the hypothesis Ho:p

Answer 1

1:

Here we have σ-10,CL- 0.95, β-0.05 Level of significance: α-0.05 Power=0.95 eer Test is two tailed so critical values are: -1.645 -1.64 21-a '-I-β -AG-AG-1 Delta: Required sample size is: =((1.645+1.64)*10/1)^2 1079.1225 Excel function for critical value: 4-α-NORMSINV(1-(0.05/2)) ZI-8-NORMSINV(1-0.05)

2:

Here we have p-0.55,p0-05, CL-0.95, β-0.1 Level of significance: α-0.05 Power-0.9 Test is one tailed so critical values are: -1.645 "I-α ~1-8 1.282 Effect Size: P120L-0.1005 Required sample size is: -2 r-1-β / I-((1.645+1.282/0.1005)^2 ES --α 7 = 848.22940026237 Hence, the required sample size is 849. Excel function for critical value: -NORMSINV(1-(0.05)) NORMSINV(1-0.1) 1-α -