Five marbles: An introduction to confidence interval hypothesis testing
Having made an error of statistical logic on Monday, I wanted to find a way to illustrate hypothesis testing without the error. I gave every student five marbles. I asked the class what the average number of marbles per student was at that point. The class understood that five was the average.
I then told them that they could either keep all five, pass one, two, three, four, or all five to a neighbor or neighbors. After the marbles were exchanged, including some rock, paper, scissors gambling with marbles as the stakes (one fellow cleaning out three neighbors of their marble stocks), I again asked what the average number of marbles is in the class. Although a couple students intuited the answer, I used an illustration using two students in the class. Even if Givelynn gives all five of her marbles to Receivelynn, the average remains five: (10+0)/2 = 5.
Each student was given a scrap of paper and told to write down the number of marbles they now had, including if they had zero marbles.
I then asked a student who arrived late to select five scraps of paper. I used the five to generate a 95% confidence interval, which included the population mean of five in each class.
H0: μ = 5
H1: μ ≠ 5
After showing that the confidence interval included the population mean of five, and that this meant we fail to reject a null hypothesis that the population mean is five, I collected the rest of the papers and calculated the population mean. After correcting a nine that I had misread as a 6, both sections had a population mean of five.
The above spreadsheet is available in Google Sheets, which now has support for the TINV function used to calculate t-critical.