Introduction: According to the M&M/Mars Company, headquartered in Hackettstown, New Jersey, the new mix of M&Ms Plain Chocolate Candies should contain 30% browns, 20% each of yellows and reds, and 10% each of oranges, greens, and blues. While the company mixes the colors as much as possible, the above ratios may vary especially in the smaller bags. This is because the various colors are combined in large quantities for the last production stage which is printing. The bags are filled on high-speed packaging machines by weight, not by count. Purpose: The purpose of this activity is to compare the actual distribution of M&Ms to the advertised ratios. A chi-squared test will be used. If this were a traditional setting classroom, I would provide you each with a bag of M&Ms. You are more than welcome to buy a bag on your own if you want and stratify by color – or use the counts provided here from a bag in an earlier semester. You want to use a chi square test to see if the proportions of the colors of M&Ms in the bag matches the company’s claimed percentages. Use p=.05 as the level of significance for this test. A. What did you conclude from the test? What was your decision (reject or Fail to reject the H0?) B. Let’s say that when you open your bag of M&Ms you find: 4 Brown, 16 Blue, 10 Orange, 8 Green, 12 Red, and 6 Yellow. Fill in the table below. Use the company ratio to determine the expected values ( E). Color Categories Brown Blue Orange Green Red Yellow Total Observed Expected (E) Deviation= (O – E) D2 = (O-E) 2 D2 / E = (O-E) 2/E X2 = ∑(O-E) 2/E
Compound Probability
Compound probability can be defined as the probability of the two events which are independent. It can be defined as the multiplication of the probability of two events that are not dependent.
Tree diagram
Probability theory is a branch of mathematics that deals with the subject of probability. Although there are many different concepts of probability, probability theory expresses the definition mathematically through a series of axioms. Usually, these axioms express probability in terms of a probability space, which assigns a measure with values ranging from 0 to 1 to a set of outcomes known as the sample space. An event is a subset of these outcomes that is described.
Conditional Probability
By definition, the term probability is expressed as a part of mathematics where the chance of an event that may either occur or not is evaluated and expressed in numerical terms. The range of the value within which probability can be expressed is between 0 and 1. The higher the chance of an event occurring, the closer is its value to be 1. If the probability of an event is 1, it means that the event will happen under all considered circumstances. Similarly, if the probability is exactly 0, then no matter the situation, the event will never occur.
Introduction:
According to the M&M/Mars Company, headquartered in Hackettstown, New Jersey, the new mix of M&Ms Plain Chocolate Candies should contain 30% browns, 20% each of yellows and reds, and 10% each of oranges, greens, and blues. While the company mixes the colors as much as possible, the above ratios may vary especially in the smaller bags. This is because the various colors are combined in large quantities for the last production stage which is printing. The bags are filled on high-speed packaging machines by weight, not by count.
Purpose:
The purpose of this activity is to compare the actual distribution of M&Ms to the advertised ratios. A chi-squared test will be used.
If this were a traditional setting classroom, I would provide you each with a bag of M&Ms. You are more than welcome to buy a bag on your own if you want and stratify by color – or use the counts provided here from a bag in an earlier semester.
You want to use a chi square test to see if the proportions of the colors of M&Ms in the bag matches the company’s claimed percentages. Use p=.05 as the level of significance for this test.
A. What did you conclude from the test? What was your decision (reject or Fail to reject the H0?)
B.
Let’s say that when you open your bag of M&Ms you find: 4 Brown, 16 Blue, 10 Orange, 8 Green, 12 Red, and 6 Yellow. Fill in the table below. Use the company ratio to determine the expected values ( E).
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Color Categories |
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Brown |
Blue |
Orange |
Green |
Red |
Yellow |
Total |
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Observed
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Expected (E) |
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Deviation= (O – E) |
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D2 = (O-E) 2 |
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D2 / E = (O-E) 2/E |
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X2 = ∑(O-E) 2/E |
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