statistics
posted by Liz .
SAT Exam Scores – A school administrator wonders if students whose first language is not English score differently on the math portion of the SAT exam than students whose first language is English. The mean SAT math score of students whose first language is English is 516, on the basis of data obtained from the College Board. A simple random sample of 20 students whose first language is not English results in a sample mean SAT math score of 522. SAT math scores are normally distributed, with a population standard deviation of 114.
(a) Why is it necessary for SAT math scores to be normally distributed to test the hypotheses using the methods of this section?
(b) Determine the appropriate null and alternative hypotheses to assess whether students whose first language is not English score differently on the math portion of the SAT exam.
(c) Use the classical or Pvalue approach at the á = 0.1 level of significance to test the hypothesis in part (b).
(d) Write a conclusion based on your results to part (c)

a. What methods were in the section? Probabilities can be calculated for a normal distribution.
b. Ho: mean 1 = mean 2
Ha: mean 1 ≠ mean 2
c. Z = (mean1  mean2)/standard error (SE) of difference between means
SEdiff = √(SEmean1^2 + SEmean2^2)
SEm = SD/√(n1)
If only one SD is provided, you can use just that to determine SEdiff.
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion related to the Z score.
d. Is that proportion from c ≤ .01 (.005 at each end)? 
ifx=76.9s=8.5compute the test statistic