Answer to Question #1544 in Statistics and Probability for Bonnie Willey

Question

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). 1. Compute Z obt 2. What is the Z critical value (Z cv ) using a 0.05 alpha level? 3. Should H0 be rejected? What should the researcher conclude? 4. Determine the 95 % con

Answer 1

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. Z_obt=√(n)(Mn-M)/σ=√(90)(1030-1000)/200=1.423
From table Zcv=1.645
Zobt< Zcv so we reject this hypothesis. And the conclusion is We have not enough evidence to take the opposite hypothesis.
4. In our case it’s one tailed test and CI=(-inf , 1.645)