Answer Happy

3. A 3rd  grade English teacher claims that the mean scores on an "art and language" assessment test for nine-year old boys is less than that of nine-year old girls. The mean score of 13 randomly selected boys is found to be xˉ1​=230.10 with a standard deviation of s1​=16.2; while those of 15 randomly selected girls are found to be xˉ2​=239.70 and s2​=12.1, respectively were the populations are approximately normally distributed and the population variances are equal. (a) Choose the appropriate hypotheses to test the science teacher's claim I. H0​:xˉ1​=xˉ2​ vs Ha​:xˉ1​=xˉ2​ II. H0​:μ1​=μ2​ vs Ha​:μ1​<μ2​ III. H0​:μ1​<μ2​ vs Ha​:μ1​≥μ2​ IV. H0​:xˉ1​≤xˉ2​ vs Ha​:xˉ1​>xˉ2​ V. H0​:μ1​=μ2​ vs Ha​:μ1​=μ2​ (b) For the above test of hypothesis, which of the following is the correct formula for the test statistics calculation? (Notice the sample sizes) I. z=n1​σ12​​+n2​σ22​​​(xˉ1​−xˉ2​)−(μ1​−μ2​)​ II. t=n1​+n2​−2(n1​−1)s12​+(n2​−1)s22​​n2​1​+n2​1​​​(xˉ1​−xˉ2​)−(μ1​−μ2​)​ III. z=s/n​x−μ​ IV. t=s/n​x−μ​ (c) Carry out the test of hypothesis by completing the remaining three steps, using α=0.05 and do not forget to circle the answers.