# **Inference for Means Activity

This activity enables students to learn about confidence intervals and hypothesis tests for a population mean. It focuses on the t-distribution, the assumptions for using it, and graphical displays. The activity also focuses on how to interpretations a confidence interval, a p-value, and a hypothesis test.

Rating:
Content Quality Concerns:
It might be helpful to re-word some of the questions on the activity so that students can make more conjectures about what they think will happen before they actually create confidence intervals or conduct a hypothesis test. Right now, it seems that students are mostly just working through steps and answering questions without taking the time to reason about why things are turning out a particular way. Also, the activity is structured in way that all calculations would be done by hand. It seems that incorporating technology of some kind--perhaps in the form of different applets--might be helpful for some students. I was further concerned about (a) why the authors talk about a sample size of 40 as being optimal (given what students may learn about the CLT--in some books--which sometimes indicates a sample of size 30 is adequate) and (b) how confidence intervals were presented in the set of suggested answers. Shouldn't students learn to state their confidence in terms of the interval and not the actually unknown population parameter?
Content Quality Strengths:
The activity is very complete and detailed, and it provides students with the opportunity to gather real-world data and explore this data in class. Rather than present confidence intervals and hypothesis tests as two separate inferential techniques, the authors attempt to help students make connections between these techniques.
Ease of Use Concerns:
There are no graphics in the student handout, and this might lead to less interest and engagement among students. Also, it is debatable how interactive the item is. Students do need to take time to read through questions and write down answers, but this might lead to rote behavior on the part of students. Adding more questions that would require them to make and test conjectures, and talk with their peers along the way, could be helpful in the long run.
Ease of Use Strengths:
The material is well organized and easy to follow, and the directions are clear. It is a nice touch to use scenario that would lead to the collection of student data in class.
Potential Effectiveness Concerns:
I'm not sure if this activity--as it is--would develop critical thinking skills or promote student discovery. Students are asked to work in pairs initially to gather some data, but then it seems like most of the rest of the activity consists of problems each student would tackle on his or her own. Further, several questions just require working through problems and coming to answers without explaining just why things are happening in a particular way. Students may come away from this activity viewing confidence intervals and hypothesis tests as consisting of steps and calculations, without really seeing the big picture. It might be helpful if somewhere along the way, students were asked to share their confidence intervals with others in class, just to get a better sense of the fact that samples vary and thus confidence intervals will vary (which relates to why we make the kinds of confidence statements we do). Also, it might be interesting to poll the class to see who rejected the null and who did not.
Potential Effectiveness Strengths:
This activity is one that can easily be completed in a single class period, and it has the potential to expose students to many important concepts and ideas all at one time. In addition, students learn about how different inferential techniques are related to one another. It appears it would be easy to write subsequent assignments or assessment questions based on some of the material in this activity in order to determine if students can transfer the knowledge they gain from this activity to new and novel situations. It encourages active learning in a relatively interesting, accessible manner.
Content Quality Rating:
4
Ease of Use Rating:
4
Potential Effectiveness Rating:
4
Source Code Available:
Source Code Available
Material Type:
Resource Type:
Statistical Topic:
Cost:
Free for Nonprofits
Format: