Final answer:
The appropriate statistical analysis for the scenario involving 40 randomly selected recent graduates to determine whether they attend college, given an 80 percent attendance expectation, is likely a proportion test or binomial test, such as a Z-test for proportions or a chi-square goodness of fit test.
Step-by-step explanation:
In the given scenario where 80 percent of the students graduating from a small Iowa farm town attend college and the town's chamber of commerce has randomly selected 40 recent graduates to inquire about their college attendance, the type of statistical analysis performed is likely a proportion test or a binomial test.
This type of analysis checks whether the observed proportion of students attending college in the sample (from the 40 selected graduates) is consistent with the expected proportion (80 percent, in this case). If a hypothesis test is being conducted, we would have a null hypothesis stating that the proportion of students from this small town attending college is the same as the expected proportion of 80 percent, versus an alternative hypothesis that it is different.
Depending on the exact nature of the analysis and the information available, techniques such as the Z-test for proportions or the chi-square goodness of fit test might be utilized to statistically analyze whether there is a significant difference between the observed sample proportion and the overall expected proportion.