Population mean for program B is not likely to be 555 -- this answer is correct! You are claiming that it is unlikely that the mean score for individuals from program B is 555. Our z-score (2.05, p <.05) indicates that the sample mean of 645 would be surprising if the population mean for Program B was truly 555. Thus, we reject our null hypothesis, meaning that we reject the assumption that Program B graduates have a mean value of 555 on the GRE. Our sample result is so surprising that it is unlikely that our sample came from a population with a mean of 555.
When we reject the null hypothesis, we reject it in favor of another explanation. This explanation is termed the alternative hypothesis. The alternative hypothesis generally states the opposite of the null hypothesis (e.g., states that the null is not true).
One last question before we move on to another sampling exercise.
Now, consider Program C. Suppose we drew a sample of 10 people from this course and obtained a mean score of 585. Which answer below best reflects the null hypothesis and conclusion based on an alpha of .05? Recall, the average score for people who took the GRE quantitative section with no training is 555 with a standard deviation of 139. Again, you will need your z-table.
a) Option 1: Null Hypothesis: Population mean = 585; Alternative Hypothesis: Population mean = 555; Do not reject null hypothesis.
b) Option 2: Null Hypothesis: Population mean = 555; Alternative Hypothesis: Population mean = 585; Do not reject null hypothesis.
c) Option 3: Null Hypothesis: Population mean = 555; Alternative Hypothesis: Population mean does not equal 555; Reject null hypothesis.
d) Option 4: Null hypothesis: Population mean = 555; Alternative Hypothesis: Population mean does not equal 555; Do not reject null hypothesis.