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. Test H_0 : mu_1 = mu_2 vs H_a : mu_1 > mu_2 using the sample results x_1 = 56, s_1 = 8.2 With n_1 = 30 and x_2 = 51 , s_2 = 6.9 With n_2 = 40. (a) Give the test statistic and the P -value. Round your answer for the test statistic to two decimal places and your answer for the P -value to three decimal places. test statistic = P -value = (b) What is the conclusion of the test? Test at a 5% level.

Explanation / Answer

Groups are independent,

SE(x1bar-x2bar)=sqrt [s1^2/n1+s2^2/n2]=sqrt[8.20^2/30+6.90^2/40]=1.85

t=(x1bar-x2bar)-0/SE(x1bar-x2bar)=(56-51)/1.85=2.70

At df=56, the pa value is 0.009.

The p value is less than alpha=0.05. Therefore, reject null hypothesis to conclude that mu1>mu2.

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