Lesson Study Log 3:
Plan the Research Lesson:
Design of the lesson
We wanted to design a lesson study that would introduce students to the idea of a confidence interval and how the compute confidence interval can be used to give information about the population parameter (here the population mean). In designing the lesson study, we wanted to emphasis how confidence intervals for the population mean are interpreted and how they should NOT be use. For example, it is common for students to believe there is 95% chance that the population mean falls in the interval or that 95% of all elements in the population fall in the confidence interval.
Outline of the lesson
1.
Pre-test on the meaning/interpretation of a confidence interval for the mean. (2-3 minutes)
2.
Discussion on the derivation of a confidence interval for the population mean. (15
- 20 minutes)
3.
Group worksheet investigating the computation of a confidence interval and the subsequent interpretation of the confidence interval. Below is a copy of the worksheet. Note: Every student has a different sample of size 30 pennies. ( 15 minutes)
MTH 145 – Elementary Statistics
Confidence Interval Worksheet
We’re going to use confidence intervals to estimate the true average age of a penny in the jar. Our population of pennies has σ = 12.62 years.
A simple random sample of 30 pennies from the jar gives the following ages in years:
30,40,22,25,21,30,14,14,40,5,5,29,26,34,2,10,13,9,3,3,53,36,20,5,21,3,3,8,11,30
For this sample of pennies, the average age is 18.83.
The formula for the confidence interval for estimating µ is x + z* (σ / n ),

where z* is the critical value for a level C confidence interval as explained in class.
Find a 68% confidence interval for the true average age of a penny (use z* = 1).
Find a 95% confidence interval for the true average age of a penny (use z* = 2).
How confident are you that the 95% confidence interval contains the true average age of all pennies in the jar?
What is the probability that your 95% confidence interval contains the true average age of all pennies in the jar?
If the true average age of the population of pennies in the jar is known to be µ = 19.92 years. Does your 68% CI contain µ?
Does your 95% CI contain µ?
.
4.
Discussion of the activity and the answers students gave to the last three questions on the worksheet. In doing so, we discussed that you are not able to apply probability statements to the confidence interval and that the confidence interval for µ tells us nothing about individuals in the population, only about the population mean. (10 minutes)
5.
Made the following table on the chalkboard and asked students to raise their hand if their computed intervals contained µ. Roughly 68% of the classes 68% CI contained µ while roughly 95% of the classes 95% CI contained µ. We then discussed the impact of the confidence level on the confidence interval. (5 minutes)
Interval contains µ Interval does not contain µ
68%
95%
Design to help students achieve learning goal.
The lesson study was developed to have students think about what a confidence interval for the population mean tells in the context of a problem (such as estimating the average age of pennies in the jar). In having the student answer various questions on their own during the activity, we were able as a class to discuss the various answers (correct and incorrect) to the questions on the worksheet. In the lesson study, students also investigated the meaning of a 68% CI and a 95% CI and the impact of the confidence level on the performance of a CI.
6.
Post - test on the meaning/interpretation of a confidence interval for the mean. (3 minutes)

Prediction
We predict that the activity will not only help students with the computation of a CI for various confidence levels, but also with the interpretation of the constructed confidence interval. With the interpretation of the CI being difficult (in comparison to the computation of the CI), we do not think this activity alone will dispel all misinterpretation of CI, but will help students to be conscience on how they interpret CI.
We believe the activity will be very successful in the objective that students will be able to compute the specified CI.
As for student interest in the lesson plan, we feel that the use of an activity will keep students engaged in the topic of confidence intervals more than a traditional lesson which consist of an entire hour of lecture.