Question

a) A significance level of $\alpha$ = 0.01 is used in testing a researcher's claim that μ > 100 and the sample data give a test statistic of z = 2.03. Determine the rejection region for this test, and then state the decision for such a test.

b) A significance level of $\alpha$ = 0.05 is used in testing a researcher's claim that μ $\neq$ 100 and the sample data give a test statistic of z = -1.85. Determine the rejection region for this test, and then state the decision for such a test.

Answer 1

Date solution - Given that, 2=0.01 za 203 Hoiu=100 Hail = 100 Test statistic 2 =2003 test This is right -tailed - P( 2 2 .03) cl-plzs 2003) = -0.9788 = 0.0212 P-value =0.0212 0.0212 >0.01 P-value za fail to reject Ho.

L=0.05 Z - 1.85 Ho! l =100 Ha; el #100 Test statistic 2 = -1.85 This is two-tailed test P-value = 2x P(Z <-1.85) -2X 0.0322 = 0.0644 P-value = 0.0644 0.0 644 > 0.05 P-value za fail to reject Ho.