Z test & One sample t-test 1. A researcher is interested in whether students who

Question

Z test & One sample t-test

1. 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 (s= 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?
The Ho should not be rejected, because the Ho is the expected value of the theory that was put together and the researcher can conclude this is a possibility.

f. Determine the 95 % confidence interval for the population mean, based on the sample mean.

Explanation / Answer

a. one-tailed b. H0: mu = 1000, HA: mu > 1000 c. z = (1030-1000)/[200/sqrt(90)] = 1.42 d. z* = 1.645 e. No. Researcher should conclude that there is no evidence private school students have higher average score than public. f. ME = 1.96*200/sqrt(90) = 41, so 989

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