Need statistics help with hypotheses testing for one population?

Posted on 2014-04-16 06:48:00 in Statistics by CORNDOG

First of all I am not asking you to do my homework. I understand how to do the problem 100%. However there is one part I don not understand.



The mean SAT scores of last year’s high school seniors was 1420. A recent sample of 165 students was taken to determine the mean SAT scores of seniors this year. The sample indicates that the mean is 1400 with a standard deviation of 100. Have this year’s SAT scores significantly decreased from last year’s? To answer this question: (1) define parameter of interest and set up the null and alternative hypotheses, (2) give the test statistic formula and its distribution, (3) give the rejection region or decision rule, (4) check any necessary assumptions and compute the test statistic, (5) make a decision. Use .01 as your significance level.



Question;

After finding the parameter of interest the teacher wrote out the null and alternative hypotheses.



1) H0: ? ? 1420

Ha: ? < 1420



2) Test stat: Z= (X – ? )/ S/ sqrt n ~ N(0,1)



My question being is in a similar problem with same assumptions she wrote H0 under Ha and on the test statistic she put ~N(0,1) under H0, by central limit theory. What why is this problem not under H0 by the CLT?

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