Posted: June 1st, 2021

# stats2

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Q1:

The plain M&M’s Milk Chocolates are mass-produced with a distribution of 24% blue, 20% orange, 16% green, 14% yellow, 13% red and 13% brown.  The peanut M&M’s are mass-produced with a distribution of 23% blue, 23% orange, 15% green, 15% yellow, 12% red and 12% brown.  So choose your favorite, rip it open and spill them out (but don’t eat any yet).  Count how many (1a) blues, (2a) oranges, (3a) greens, (4a) yellows, (5a) reds and (6a) browns are in your package.  What percentage of the package are (1b) blues, (2b) oranges, (3b) greens, (4b) yellows, (5b) reds and (6b) browns?
Create a pie chart or bar chart showing the distribution.  Now you cannot expect your package to have exactly the same percentages as the population, but it probably will be similar.
After you report your totals, tell me whether you believe your package seems about right, and if not, what stands out (like there are hardly any greens or there are mostly reds).  Now you can eat the evidence.
After each student has posted their results, the instructor will summarize the findings.  This activity will count as part of the discussion grade, as the postings will be in the discussion forum.

Q2:
“The larger the sample, the more reliable the results.”   Do you agree or disagree with this statement?  Explain.

Q3
An auto manufacturer advertises that “90% of the cars we’ve ever made are still on the road.”

Assuming this is literally true, how can it be explained?
What facts / statistics would you need to know to expose this misleading claim?

Q4

1.69 ounce pack of M&M’s. Rip open a corner but don’t pour them out this time.  You are going to pour our several samples.  The focus here is on the Blue candies.  Approximately 1 out of every 4 in both the plain and peanut M&M’s are blue.

1st sample)  Pour out 4 candies.  (1) Count and record the total blues.  Probability dictates that there should be 1 blue, but in a small sample anything can happen, and the results are random.
2nd sample)  Pour out 8 candies.  (2) Count and record the total blues.  Probability dictates that there should be 2 blues, but we shall see.
3rd sample)  Pour out 12 candies.  (3) Count and record the total blues.  Probability dictates that there should be 3 blues, and you are probably wondering why you are counting instead of eating.
4th sample)  Pour out 16 candies.  (4) Count and record the total blues.  Probability dictates that there should be 4 blues, and you can’t believe you are holding so many delicious candies in your hand at once.
5th sample) There should be anywhere from 13 to 17 candies left in the package, so tell me (5a) how many were left and (5b) how many of them were blue.
Total package)  Add up your totals.  (6a) How many candies were in the package and (6b) how many of them were blue.  How close was it to one-fourth of the package?  Were each of the samples consistent or did they vary a bunch?
In case you are wondering, you are burning calories while you are doing this mental exercise (hint, hint!).
After each student has posted their results, the instructor will summarize the findings.
This activity will count as part of the discussion grade, as the postings will be in the discussion forum.

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