QUESTION SCENARIO:

Students applying to graduate schools in many disciplines are required to take the Graduate Record Examination (GRE). An ambitious undergraduate student creates a study program that she believes will greatly increase students' GRE scores, relative to the general population. She recruits a sample of 100 students believed to be representative of the larger undergraduate student population and puts them through the study program. Afterwards, they complete the GRE and receive a mean score of M = 720. The population of GRE scores is normally distributed with a mean of = 1100 and a standard deviation of = 200.

b) An analysis conducted to determine whether the GRE scores for a sample of students who completed this program were higher than the general population yielded z = 2.24, p= .025. If the researcher uses a = .01 as their criteria for identifying a significant difference or effect, what decision would they make about the null hypothesis and why?

ANSWER to B: The z-score of 2.24 indicates that the mean GRE score of the sample is 2.24 standard deviations above the population mean, which is a large effect size. The small p-value (0.025) indicates that there is a less than 1% chance of obtaining a sample mean as extreme as 720 if the null hypothesis were true. Additionally, the researcher can confidently conclude that the study program has a significant effect on GRE scores. Therefore, the researcher would reject the null hypothesis.

QUESTIONS I AM HAVING TROUBLE WITH:

c) What would you conclude based on the results of the analysis conducted in question b? (i.e., relate your decision about the null hypothesis back to the research hypothesis)

d) Would the decision about the null hypothesis from question b change if the researcher useda = .05 for the test? Why or why not?