1. http://www. ltcconline

2. Is my sample of M & M’s unusual?

3. Fill out this table for YOUR sample of M & M’s
Color
Obs Count
Blue
Orange
Green
Yellow
Red
Brown
Total
Fill out this table for YOUR sample of M & M’s
Mars and Murrie invented the candy coated chocolate candy for the military in the 40’s so that soldiers could carry a quick energy ration that would not melt in the tubes that the candy came in.  (This sugar coating is the same that was used on medicines at the time…)
When these soldiers came back from the war the candy proved to be popular and so the candy was produced for sale.  These were called M & M’s but the stamping of the candy with the initials did not occur until later.

4. Color Obs Count Pop % Expected Count Blue 24% Orange 20% Green 16%
Yellow
14%
Red
13%
Brown
Total
The M & M activity is not to test  if M & M is lying about their percentages.  Each student is going to get a chi-square value that measures how unusual their bag actually is.  We could make a bingo-marker dot plot of each of their values and produce a simulated chi-square distribution for df = 5.  (In fact, I’ve decided to do this just now.)
A lot of kids will get a p-value that is really, really small.  They’d reject the null.  But, M&M Mars isn’t lying about their percentages.  Our observed data are different than what we expected because either (1) we drew an unusual sample due to chance or (2) we violated one of the assumptions of the test .  We’ve got both happening here because I scooped out some samples purposely grabbing certain colors.

5. Introduction to the 𝜒2 test
(Read as a chi-squared test)
Pronunciation guide:
You could say chi (like sky)
(that’s how I’ve always heard it!)
You could say chi (like key)
(which is apparently how the Greeks say it)

7. Conditions for a 𝜒2 test Ready? Randomly selected sample 10n < N
All expected counts at least 5

8. The Χ2 Distribution Χ2 ≥ 0 Asymptotic to horizontal axis
Family of curves denoted by……df!

9. Example 2:
Are fatal bicycle accidents equally likely throughout the 24-hour period of a day?

10. Time of Day
# of Accidents
Expected Values
Midnight ― 3:00 a.m. 38
3:00 a.m. ― 6:00 a.m. 29
6:00 a.m. ― 9:00 a.m. 66
9:00 a.m. ― Noon 77
Noon ― 3:00 p.m. 99
3:00 p.m. ― 6:00 p.m.
127
6:00 p.m. ― 9:00 p.m.
166
9:00 p.m. ― Midnight
113
715

12. Example 3: Who Buys Lotto Tix?
Age distribution of adults in California:
35% between 18 and 34 years old
51% between 35 and 64 years old
14% are 65 years or older
In an SRS of 200 adults in California:
36 between 18 and 34 years old
130 between 35 and 64 years old
34 of those 65 years or older
bought Lotto Tickets