Question

**M&M's Color Distribution:** Suppose the
makers of M&M candies give the following average percentages
for the mix of colors in their bags of plain chocolate
M&M's.

Stated Distribution of Colors

Brown | Yellow | Red | Orange | Green | Blue | |

Percent | 30% | 20% | 20% | 10% | 10% | 10% |

Now, you randomly select 200 M&M's and get the counts given in the table below. You expected about 20 blues but only got 9. You suspect that the maker's claim is not true.

Observed Counts by Color (* n* = 200)

Brown | Yellow | Red | Orange | Green | Blue | |

Count | 64 | 33 | 44 | 27 | 23 | 9 |

**The Test:** Test whether or not the color of
M&M's candies fits the distribution stated by the makers (Mars
Company). Conduct this test at the 0.01 significance level.

(a) What is the null hypothesis for this test in terms of the probabilities of the outcomes?

*H*_{0}: *p*_{brown} =
*p*_{yellow} = *p*_{red} =
*p*_{orange} = *p*_{green} =
*p*_{blue} = 1/6*H*_{0}: At least one
of the probabilities doesn't fit the company's
statement. *H*_{0}: The
probabilities are not all equal to
1/6.*H*_{0}: *p*_{brown} =
0.30, *p*_{yellow} = 0.20, *p*_{red}
= 0.20, *p*_{orange} = 0.10,
*p*_{green} = 0.10, and *p*_{blue} =
0.10.

(b) What is the value of the test statistic? **Round to 3
decimal places unless your software automatically rounds to 2
decimal places.**

*χ*^{2}

=

(c) Use software to get the P-value of the test statistic.
**Round to 4 decimal places unless your software
automatically rounds to 3 decimal places.**

P-value =

(d) What is the conclusion regarding the null hypothesis?

reject *H*_{0}fail to reject
*H*_{0}

(e) Choose the appropriate concluding statement.

We have proven that the distribution of candy colors fits the maker's claim.The data suggests that the distribution of candy colors does not fit the maker's claim. There is not enough data to suggest that the distribution of candy colors is different from what the makers claim.

Additional Materials

Answer #1

Category | pi | Observed Freq. (Oi) | Expected Freq. (Ei) | (Oi - Ei)^2/Ei |

Brown | 0.3 | 64 | 60 | 0.267 |

Yellow | 0.2 | 33 | 40 | 1.225 |

Red | 0.2 | 44 | 40 | 0.400 |

Orange | 0.1 | 27 | 20 | 2.450 |

Green | 0.1 | 23 | 20 | 0.450 |

blue | 0.1 | 9 | 20 | 6.05 |

200 | 10.842 |

b)

chi-square = 10.842

c)

p-value = 0.0546

d)

fail to reject H0

e)

There is not enough data to suggest that the distribution of candy
colors is different from what the makers claim.

M&M's Color Distribution: Suppose the
makers of M&M candies give the following average percentages
for the mix of colors in their bags of plain chocolate
M&M's.
Stated Distribution of Colors
Brown
Yellow
Red
Orange
Green
Blue
Percent
30%
20%
20%
10%
10%
10%
Now, you randomly select 200 M&M's and get the counts given
in the table below. You expected about 20 blues but only got 9. You
suspect that the maker's claim is not true.
Observed Counts by Color...

M&M's Color Distribution: Suppose the
makers of M&M candies give the following average percentages
for the mix of colors in their bags of plain chocolate
M&M's.
Stated Distribution of Colors
Brown
Yellow
Red
Orange
Green
Blue
Percent
30%
20%
20%
10%
10%
10%
Now, you randomly select 200 M&M's and get the counts given
in the table below. You expected about 20 blues but only got 9. You
suspect that the maker's claim is not true.
Observed Counts by Color...

M&M's Color Distribution: Suppose the
makers of M&M candies give the following average percentages
for the mix of colors in their bags of plain chocolate
M&M's.
Stated Distribution of Colors
Brown
Yellow
Red
Orange
Green
Blue
Percent
30%
20%
20%
10%
10%
10%
Now, you randomly select 200 M&M's and get the counts given
in the table below. You expected about 20 blues but only got 10.
You suspect that the maker's claim is not true.
Observed...

Suppose the makers of M&M candies give the following average
percentages for the mix of colors in their bags of plain chocolate
M&M's.
Stated Distribution of Colors
Brown
Yellow
Red
Orange
Green
Blue
Percent
30%
20%
20%
10%
10%
10%
Now, you randomly select 200 M&M's and get the counts given
in the table below. You expected about 20 blues but only got 8. You
suspect that the maker's claim is not true.
Observed Counts by Color...

M&M's Color Distribution: Suppose the
makers of M&M candies give the following average percentages
for the mix of colors in their bags of plain chocolate
M&M's.
Stated Distribution of Colors
Brown
Yellow
Red
Orange
Green
Blue
Percent
30%
20%
20%
10%
10%
10%
Now, you randomly select 200 M&M's and get the counts given
in the table below. You expected about 20 blues but only got 9. You
suspect that the maker's claim is not true.
Observed Counts by Color...

Upon request, the Mars Company (the maker of M&M's) will
provide the color distribution for their candies. As of August
2009, they noted that
"Our color blends were selected by conducting consumer
preference tests, which indicate the assortment of
colors
that pleased the greatest number of people and created the most
attractive overall effect.
On average, our mix of colors for M&M'S CHOCOLATE CANDIES
is:
M&M'S MILK CHOCOLATE: 24% cyan blue, 20% orange, 16% green,
14% bright yellow, 13% red,...

A package of 100 candies are distributed with the following
color percentages: 12% red, 22% orange, 14% yellow, 12%
brown, 24% blue, and 16% green. Use the given sample data to test
the claim that the color distribution is as claimed. Use a 0.025
significance level.
Candy Counts
Color
Number in Package
Red
1313
Orange
2727
Yellow
66
Brown
1010
Blue
2727
Green
17
The test statistic is
(Round to two decimal places as needed.)
The critical value is
(Round...

Several years ago, the Mars, Incorporated website reported the
following percentages of the various colors of its M&M'S
candies for the "milk chocolate" variety.† A graphical display
lists 6 colors. Beside each color is a picture of an M&M with
the percentage listed below the picture. The colors and percentages
are as follows. Brown: 13% Yellow: 14% Red: 13% Blue: 24% Orange:
20% Green: 16% A 14-ounce bag of milk chocolate M&M'S is
randomly selected and contains 71 brown, 75...

Several years ago, the Mars, Incorporated website reported the
following percentages of the various colors of its M&M'S
candies for the "milk chocolate" variety.†
A graphical display lists 6 colors. Beside each color is a
picture of an M&M with the percentage listed below the picture.
The colors and percentages are as follows.
Brown: 13%
Yellow: 14%
Red: 13%
Blue: 24%
Orange: 20%
Green: 16%
A 14-ounce bag of milk chocolate M&M'S is randomly selected
and contains 72 brown, 74...

According to Mars Inc., the distribution of colors of the
M&M candies is Brown- 13 Yellow- 14 Red- 13 Blue- 24 Orange- 20
Green-. 16.Several bags were randomly chosen and the percentages of
each color were found to be as follows: Brown – 15.3%, Yellow
–18.1%, Red – 11.7%, Blue – 19.8%, Orange – 22.6%, and Green –
12.5%. According to this sample, does it appear that the
distribution of colors does not fit what’s expected, according to
the manufacturer’s...

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