Use the t distribution and the given sample results to complete the test of the

Question

Use the t distribution and the given sample results to complete the test of the given hypotheses. Assume the results come from random samples, and if the sample sizes are small, assume the underlying distributions are relatively normal. H_0: mu_1 = mu_2 vs H_a: mu_1 notequalto mu_2 using the sample results X_1 = 15.3, s_1 = 11.6 with n_1 = 100 and X_2 = 18.4, s_2 = 14.3 with n_2 = 80 Give the test statistic ______ Give the P value ______ What is the conclusion of the test? Test at a 10% level. Reject H_0 or Do not reject H_0.

Explanation / Answer

from above data

degree of freedom v=((s12/n1+s22/n2)2/((s12/n1)2/(n1-1)+ (s22/n2)2/(n2-1))=150 (by rouding it down)

std error =(s12/n1+s22/n2)1/2 =1.975

hence test stat =(X1-X2)/std error =-1.569

for above tstat and at 150 df ; p value =0.1187

as p value is above 10% level, we can not reject null hypothesis.

S1 11.600 S2 14.300 n1 100 n2 80 X1 15.300 X2 18.400

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