COC Math 140 Confidence Interval Partner Activity

Did I capture the true population parameter?

Go to my website and copy/paste (from COC Math 140 Survey Data Spring 2016) column G (hair color data) into Stat Crunch. In this data set, n = 371. Using the random number generator in Stat Crunch, randomly choose 10 entries from the data (go to Applets, Random Numbers, minimum = 1; maximum = 371; sample size = 10; do not allow repeats).

Enter/Type these 10 randomly-selected hair colors into another list (type them into a list of their own; be careful to spell all 10 hair colors correctly and consistently). Now, let’s create a 95% confidence interval for the true, unknown proportion of all COC Math 140 students (Spring 2016) who reported they had brown hair ONLY USING YOUR 10 RANDOMLY-SELECTED PIECES OF DATA.

In Stat Crunch, go to Stats, Proportion Stats, One Sample, With Data.

Choose YOUR LIST WITH 10 VALUES IN IT, NOT THE COLUMN WITH THE 371 PIECES OF DATA IN IT. For ‘success,’ type in Brown (that’s what we are creating a confidence interval about).

Select ‘confidence interval’ and type in 95% for our confidence level. Compute. Write your confidence interval (lower limit, upper limit) on the board. You do not have to write any context for this activity.

After we have all our confidence intervals on the board, we will discuss the following questions (be ready to comment on them):

  1. Did we all get the same confidence intervals (i.e., do they all have the same lower limit and the same upper limit)? Why or why not?
  1. Are they all the same width? Why or why not? What is our margin of error? Are all our estimators the same?
  1. How do our confidence intervals compare to the true, unknown population proportion for ALL COC Math 140 Spring student data? How could we find our true population parameter for all of these 371 Math 140 students? Did all of our confidence intervals ‘capture’ the true population parameter or not? Why or why not?
  1. Would it make sense for us to calculate a confidence interval using all 371 Math 140 students to estimate the true, unknown population proportion for all Math 140 Spring students? Why or why not?

BIG IDEAS to take away from this activity are (please list 2-3 big ideas below):