B. Two Sample Hypothesis Test To compare the difference between two means, propo

Question

B. Two Sample Hypothesis Test To compare the difference between two means, proportions or variances, we must use hypothesis tests. The overall process is very similar to hypothesis tests with one sample. First, set up your null and alternate hypotheses. As before, the statement you are trying to prove (eg. . 2) should be your alternative hypothesis, and your null hypothesis should be that there is no difference between the two sam ples (e.g. -). Alternatively, the example hypotheses can be stated as a. D18i Find the critical value: Use or a/2 depending on whether the test is one-tailed or two- tailed. c. Find your p-value using the appropriate formula Test Critical value one t zscorc at zscore at /2 (ol and 2 known) (Xi -X2) - (1 2) tscore at /2 tscore at (ol and 2 d.f.=smaller ofnrI or n-1 tscore at /2 | df-smaller ofnrI or n-1 tscore at D-HD dependent samples T df=n-1 where D=Differences/n average difference | df-smaller ofnrI or n2- test (Paired T-and so(nD-(D)n(n-1)) test Two proportion Z test Zscore at a2 Zscore at where p-(XitX(n +n) and q-l Two sample variance F The larger of two variances placed intersection of F-table score at intersection of numerator df. F-table score at 1 numerator df= n-1 and denominator df.=n-1 for the given a2 test on Top d.f. for the given

Explanation / Answer

Sol(A):

Conclusion: Z-value greater than critical value , therefore we reject null hypothesis.

Sol(D):

Conclusionn: t(Calculated)<t(tabulated)

Therefore no evidence to reject null hypothesis.

Sample Mean 1 121 Sample Mean 2 112 Difference in Mean 9 Variance 1 64 Variance 2 64 Sample size 1 10 Sample size 2 10 z-value 2.577 Critical value 1.96 P-value 0.010

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