Statistical Comparison of Reading Comprehension Test Scores: Private vs. Public School Eighth-Graders
Comparative statistical analysis of reading comprehension in different school systems.
Caleb Patterson
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Statistical Comparison of Reading Comprehension Test Scores: Private vs. Public
School Eighth-Graders
Scenario:
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 taken
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.
The independent variable is the type of school, whether private or publicly funded. The
dependent variable here is test score of eighth-grade students.
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).
Null hypothesis, H0: The mean test score of eighth-grade students attending private middle
schools is 204.2, i.e. mean test score of eighth-grade students attending publicly-funded
schools, i.e. μ = 204.2.
School Eighth-Graders
Scenario:
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 taken
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.
The independent variable is the type of school, whether private or publicly funded. The
dependent variable here is test score of eighth-grade students.
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).
Null hypothesis, H0: The mean test score of eighth-grade students attending private middle
schools is 204.2, i.e. mean test score of eighth-grade students attending publicly-funded
schools, i.e. μ = 204.2.
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