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Answer to Question #1551 in Statistics and Probability for Misty Cooke

Question #1551
& A researcher is interested in whether students who attend private high schools have higher average SAT Scores than students in the general population. A random sample of 90 students at a private high school is tested and and a mean SAT score of 1030 is obtained. The average score for public high school student is 1000 (σ= 200).
Expert's answer
1. This is a one tailed test because theprediction is that the private high school students will have higher scores, thusthere is a bias.
2. The Hypothesis – or the Ha = that the private high school students will have a higher average SAT Score than the students in the general population.
The Null Hypothesis – or the Ho = that the private high school students will not have a higher average SAT score than the students of the general population.
3. Zobt=√(n)(Mn-M)/σ=√(90)(1030-1000)/200=1.423
4. From table Zcv=1.645
5. Zobt< Zcv so we rejected this hypothesis. And the conclusion is We have not enough evidence to take the opposite hypothesis.
6. In our case it’s one tailed test and CI=(-inf , 1.645)

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