1. A researcher is interested inwhether students who attend private high schools
ID: 2954938 • Letter: 1
Question
1. A researcher is interested inwhether students who attend private high schools have higheraverage SAT Scores than students in the general population. Arandom sample of 90 students at a private high school is tested andand a mean SAT score of 1030 is obtained. The average score forpublic high school student is 1000 (= 200).
a. Is this a one- or two tailedtest?
b. What are H0 andHa for this study?
c. Compute Z obt
d. What is the Z critical value (Zcv ) using a 0.05 alpha level?
e. Should H0 berejected? What should the researcher conclude?
f. Determine the 95 %confidence interval for the population mean, based on the samplemean.
Explanation / Answer
a. Is this a one- or two tailedtest?
One-tailed test
b. What are H0 andHa for this study?
Ho:<=1000
Ha:>1000
c. Compute Z obt
Z=(xbar-)/(/n)
=(1030-1000)/(200/sqrt(90))
=1.42
d. What is the Z critical value (Zcv ) using a 0.05 alpha level?
Z(0.05)=1.645 (check normal table)
e. Should H0 berejected? What should the researcher conclude?
Since Z=1.42<1.645, we do not reject Ho. So we can notconclude that students who attend private high schools have higheraverage SAT Scores than students in the generalpopulation.
f. Determine the 95 %confidence interval for the population mean, based on the samplemean.
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