11.1 Paired two sample t-yest for a difference of sample means

I went with the light blue marbles for no particular reason. Although the mean for the marbles is typically between 5.1 and 5.2 grams, a split based on that yielded too few heavy marbles. The light blue marbles split roughly 27 light and 24 heavy on a split between 5.0 and 5.1.

Marbles 5.0 or lighter on one side 5.1 or heavier on the other. Spring term I excluded 5.0 and 5.1 marbles, but that also necessitated using a mix of colors. And that eliminated the finding that students might be able to detect differences of 0.1 grams. Spring term had a very small sample size which actually proved educational as the seventh student stopped the p-value below 0.05. That said, the spring term also came within one pair of a 100% success rate which would be too good a result in some sense. I want something that has a sense that random luck achieved whatever result was obtained. 

At 13 students the p-value was 0.09 and we failed to reject the null hypothesis.

Two students arrived late and both correctly ascertained which marble was more massive. 

This dropped the p-value to 0.03 and changed the result to being statistically significantly different and the null hypothesis is rejected.

The spreadsheet used the FORMULATEXT function for the first time. This meant that when the function in F7 was edited, the formula shown in H7 automatically updated. 

Once again the impact of late arrivals well illustrated the impact of sample size by reversing the results. The complication is that a Bonferroni correction would drop alpha to 0.025 and 0.027 just comes in over the adjusted alpha. Explaining this to the students would be a very confusing bridge too far. That the results reversed upon the arrival of Emylia and John was confusing for the students. Throwing in a Bonferroni correction would have been too much. 

This remains an interesting exercise especially in that once the sample size is large enough, the null hypothesis is usually rejected.