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Answer to Question #1031 in Statistics and Probability for Billy Hood

Question #1031
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).

a. Is this a one- or two tailed test?

b. What are H0 and Ha for this study?

c. Compute Z obt

d. What is the Z critical value (Z cv ) using a 0.05 alpha level?

e. Should H0 be rejected? What should the researcher conclude?

f. Determine the 95 % confidence interval for the population mean, based on the sample mean.
Expert's answer
a. It's two-tailed test.

b.
Ho : the average score of the public school equals to the mean score.
Ha : the mean score of the public school is not equal to the mean score.

c. z=(1000-1030)/(200/√90) = -1.42;

d. Zcv = 1.96

e. 1.42 < 1.96 - we cannot reject the null hypothesis. The average score of the public school can be equal to the 1030.

f.
the upper limit : 1030 + 1.96*(200/√90) = 1071.32
the lower limit: 1030 - 1.96*(200/√90) = 988.68

d. p(z = -1.42) = 0.1556 > 0.05

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