Wrapping up:  Common errors by students for the last two FR questions for our end-of-year assignment.

Question 5: In this question,we wanted students to construct correct hypotheses for a test,  state/ compute the correct test statistic,  and make an appropriate decision about their hypotheses in context. In addition, students needed to use the results of a simulated sampling distribution to make a conclusion about a hypothesis test “outside the AP syllabus.”  The topic:  bottle filling machines.

• Students need to define the population parameter of interest thoroughly.  They must refer to the correct symbol,  The population(s) (or treatment(s)) of interest, and the correct parameter name (the true mean amount,  the true proportion of people who agree).  Students often left out at least one of these.  
• Students over-stated their conclusions when failing to reject a null hypothesis. A high p-value does not give you evidence that Ho is true.  They sometimes accidentally make  this conclusion when adding context.
• Students give incomplete mechanics, especially omitting the degrees of freedom. If a ch-squared or t-procedure s called for, degrees of freedom  are needed in the mechanics.
• Bottom Line:  get the details down. 

Students’ seem to have an incomplete understanding of simulated sampling distributions. After grading the “interpret a simulation” part of the  question, I wondered if students got full credit simply by “going through the motions” of getting an estimated p-value  via simulation without being able to answer a deeper question, or one that was phrased differently.  They got the “key points,”  but then made some conceptual errors about what the null hypothesis was, failing to distinguish sample SD from population SD, etc.

Question 6: In this question,  the goal was for students to read a scenario and a) cite specific evidence from equations or graphs to justify a statement about expected returns,  b) construct a confidence interval for a population proportion (and verify conditions),  c) apply an understanding of the interval to justify a real-world decision and d) synthesize all previous work to construct a statistically reasonable rationale for an alternate conclusion.  Topic: Deciding to use vans or coach buses for a business.

Common errors:

• Students struggle to articulate specific evidence from a graph.  They usually said something equivalent to this: “by just looking at the graph, we can see vans are better.”  It was difficult for students to identify specific evidence from the graph that supported their claim.
• Students did not give a correct “normality” check for a 1 proportion confidence interval. Many erroneously checked the “n>30” condition for means.  Others omitted the check altogether.
• Students got sloppy interpreting the confidence interval in correct context.  They gave the wrong population, the wrong variable, or referred to the wrong parameter (the mean of the population  or “mean proportion of all samples”  instead of the proportion of all markets that will experience strong demand.

Advice for my students:  

• Review technical details.  Do problems about probability, sampling distributions, binomial distributions, run the details of each of the major tests.  Learn the “large sample. normality” condition of each test.  Practice choosing the correct test at this site.