## Intro Stats Final Exam Using StatCrunch

Last week I gave my final exam using StatCrunch, and I’m quite pleased with the results.

### Overcoming Anxiety

I was a little nervous about this exam. Will there be enough time? What if we lose power? What if my students are not as prepared as I think?

Our college schedules 2-hour final exams. My exam was made up of 10 problems – 2 confidence intervals and 8 hypothesis tests – and time ended up not being an issue. Most students took approximately 1 hour to complete the exam.

My contingency plan for power loss was to provide students with p-values for each test, essentially I would take the role of StatCrunch. Not ideal, but my students could take my information and complete their exam.

My students, as a group, were well prepared.

• One class had 31 students take the exam, and they all passed. There were 18 A’s, 10 B’s, and 3 C’s. The median score was 93.
• The other class had 39 students take the exam, and 32 passed the exam. There were 21 A’s, 9 B’s, 2 C’s, 2 D’s, and 5 F’s (47, 44, 22, 22, 10). The median score was 91. The students who earned F’s had been performing poorly heading into the exam, and as a rule struggled with identifying the appropriate test and writing up the 5 step hypothesis test.

### Format of the Exam

As I mentioned earlier, there were 2 confidence intervals and 8 hypothesis tests. We had covered 3 confidence intervals (one mean z, one mean t, and one proportion) and 10 hypothesis tests (one mean z, one mean t, one proportion, paired difference, two mean, two proportion, two variance, goodness of fit, chi square independence, ANOVA). Some of the problems provided summary data, while others provided raw data.

For confidence interval problems, students had to explain exactly what the confidence interval told them in their own words.

For hypothesis test problems, students had to write up a 5 step hypothesis test.

1. H0 and H1, as well as H1 in words
2. Level of significance
3. Test being performed
4. Decision rule (p-value approach)
5. Test stat and p-value from StatCrunch, Decision about H0, Conclusion about H1

There were also follow up questions after each test. Examples include “Is this a z-test or a t-test? Explain your answer fully.”, “Do your results prove that the mean for City A is greater than the other 3 cities? (ANOVA)”, “Do your results prove that 75% of working mothers purchase take-out food each week?”

To answer these questions, students need to completely understand the hypothesis testing procedure and exactly what each test is testing. For instance, students need to understand that we either reject or fail to reject H0, we never support that statement. Students need to understand whether two variables are related based on the chi-square goodness of fit test.

As I graded their exams, I was relieved that the students were successful in identifying the proper test and getting the correct results from StatCrunch. But what made me smile was that they were so successful with my follow up questions.

### Summary

I am so pleased with my use of StatCrunch! I plan to take another giant step when I teach this course again. In the early part of the course, I will spend less time on calculation and more time on interpretation and big picture ideas. I will fully incorporate the probability distribution calculators rather than relying on formulas and tables. I will teach confidence intervals with each hypothesis test. And I will cover more hypothesis tests and regression.

Do you use StatCrunch, or some similar technological tool, in your statistics courses? Would you like to share your approach, and particularly your exam strategies, with other instructors? Do you have any questions on StatCrunch? Would you like a copy of my exam? If so, please leave a comment or reach me through the contact page at my web site – georgewoodbury.com.

-George

I am a math instructor at College of the Sequoias in Visalia, CA. If there’s a particular topic you’d like me to address, or if you have a question or a comment, please let me know. You can reach me through the contact page on my website – http://georgewoodbury.com.