# A researcher asks if eighth-grade students attending a private middle school

August 30, 2017

Question
A researcher asks if eighth-grade students attending a private middle school have higher or lower scores on a test of reading comprehension when compared to the population of eighth-graders attending publicly-funded schools. A sample of 144 private school eighth-graders take the same exam that all public school 8th graders take at the end of the school year. The private school students have a mean test score of 220.8 and the mean score for the public school students is 204.2, with a standard deviation of 11.4.

State the independent and dependent variables and explain how you know which is which.
Explain whether the researcher should use a one-tailed or a two-tailed z test and explain why.
State the null hypothesis in words (not formulas).
State the alternative hypothesis in words (not formulas).
Calculate the obtained z score by hand. Provide your calculations in your Assignment submission (i.e., show your work).
When alpha is set at .05, the critical value is ± 1.96. Would you retain or reject the null hypothesis? Explain why?
Are the results significant? How do you know?
What should the researcher conclude about the reading comprehension of the private school students in comparison to the population?
In general, explain the relationship between z scores and the standard deviation.

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