Question: We have already discussed summary parameters for CFC scores for the population of participants in a study by Petrocelli (2003). The mean CFC score was 3.51, with a standard deviation of 0.61. (Remember that even though this was a sample, we treated the sample of 664 participants as the entire population.) Imagine that you randomly selected 40 people from this population and had them watch a series of videos on financial planning after graduation. The mean CFC score after watching the video was 3.62. We want to know whether watching these videos might change CFC scores in the population. But we start by standardizing this mean so that we can make comparisons.
a. Why would it not make sense to compare the mean of this sample with the distribution of scores? Be sure to discuss the spread of distributions in your answer.
b. In your own words, what would the null hypothesis predict? What would the research hypothesis predict?
c. Using symbolic notation and formulas, what are the appropriate measures of central tendency and variability for the distribution from which this sample comes?
d. Using symbolic notation and the formula, what is the z statistic for this sample mean?
e. Roughly, to what percentile does that z statistic correspond?