The goal of this paper is to test a hypothesis that the attendance of a private school influences students’ performance on a test of social skills as compared to the results of public high schools students.
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The direction of the relationship is insignificant for testing this hypothesis, thus, a researcher can perform a 2-tailed test for identifying what the treatment changes without predicting the direction of the changes that occur.
The alternative or scientific hypothesis (H1) for this research states that the independent variable of attending a private or a public school has an effect on the dependent variable of students’ performance on a test of social skills. The alternative hypothesis does not specify whether the effect of treatment would increase or decrease the test scores.
The null hypothesis (H0) states the opposite to the assertion of the scientific hypothesis. Gravetter and Wallnau (2008) noted that “The null hypothesis states that the treatment has no effect” (p. 192). In particular, the null hypothesis for this research is that there is no relationship between students’ attendance of a public or a private school and their performance on a test of social skills.
Analyzing the data from the samples, a researcher should decide whether it provides the support for the null hypothesis or contradicts it. Considering the standard deviation of experimental data, a researcher should conclude whether the range of deviation between the population mean (m) for students from public high schools and private high schools is statistically significant, conducting the Z test and deciding whether the sample is typical of the population by comparing the “Z obtained” (Zobt) and “Z critical” (Zcrit). Taking into account that Zobt= -1.54 and Zcrit= 1.96, a researcher can conclude that Zcrit>|Zobt|. It means that the researcher can accept the null hypothesis, rejecting the alternative one.
The results of the survey are statistically insignificant, because Zobt is less than Zcrit, and the researcher cannot use this data for supporting the alternative hypothesis. There is no significant relationship between attendance of a private or a public school and high student’s performance on a test of social skills.
A type I error occurs if a researcher rejects a null hypothesis which appears to be true, it is false positive (α). In case if only the weakest or only the strongest students have been present in the 100 of the sample population, it would influence the results of the survey significantly.
Some students could produce Zobt above or below 1.96 under normal circumstances in about 5% of the cases. It means that the probability that the null hypothesis is true but was rejected is 0.05 or 5 %. If a type I error was made, it means that there is no significant relationship between the type of the school and the students’ performance on a test of social skills.
A type II error occurs if a researcher accepts a null hypothesis which happens to be false, it is false negative (β). It is possible that there is a significant difference between performance of students of private and public schools, but the chosen sample did not reflect this difference. If a type II error was made, it means that the relationship between attendance of a public or a private school exists but was not identified because of not identical distributions of students with various levels of abilities.
Cohen, B. and Lea R. (2004). Essentials of statistics for the social and behavioral sciences. Danvers, MA: John Wiley and Sons.
Gravetter, F. and Wallnau, L. (2008). Essentials of statistics for the behavioral sciences. Belmont, CA: Thomson Learning.