Question

1. Objective: To determine how well a categorical sample distribution fits into a claimed population distribution.

All plain M&Ms in the U.S. are manufactured at two different factories—one in New Jersey, and one in Tennessee. The factories produce different color distributions, as shown below.

Professor Gomez buys a 3.14oz bag of M&M’s. Of the 112 M&M’s in the bag, there were 30 blue, 26 orange, 25 green, 9 yellow, 18 red, and 4 brown.

(a) Fill out the tables below with the expected values at each factory.

                  

Tennessee Factory
Color	Observed	Expected
Blue	30
Orange	26
Green	25
Yellow	9
Red	18
Brown	4

New Jersey Factory
Color	Observed	Expected
Blue	30
Orange	26
Green	25
Yellow	9
Red	18
Brown	4

(b) Use expected values from the New Jersey factory to perform a goodness-of-fit test with α = 0.01.

Check the assumptions:

Calculate the test statistic  =  by completing the following table:

Color
Blue	30
Orange	26
Green	25
Yellow	9
Red	18
Brown	4

Critical Value =  =

Decision:

(c) Use the expected values from the Tennessee factory to perform a goodness-of-fit test with α = 0.01.

Check the assumptions:

Use the GOF-Test on your graphing calculator to find the test statistic.  ____________

Critical Value =  =

Decision:

(d) According to the goodness-of-fit tests, where was this bag of M&Ms likely manufactured

Answer 1

(a) Fill out the tables below with the expected values at each factory.

                  

Tennessee Factory
Color	Observed	Expected
Blue	30	18.67
Orange	26	18.67
Green	25	18.67
Yellow	9	18.67
Red	18	18.67
Brown	4	18.67

New Jersey Factory
Color	Observed	Expected
Blue	30	18.67
Orange	26	18.67
Green	25	18.67
Yellow	9	18.67
Red	18	18.67
Brown	4	18.67

(b) Use expected values from the New Jersey factory to perform a goodness-of-fit test with α = 0.01.

Check the assumptions: yes the assumptions are met because all expected value is greater than 5

New Jersey Factory
Color	Observed	Expected	chi square contribution
Blue	30	18.67	6.875678
Orange	26	18.67	2.87782
Green	25	18.67	2.146165
Yellow	9	18.67	5.008511
Red	18	18.67	0.024044
Brown	4	18.67	11.52699
		sum	28.45921

Calculate the test statistic  = 28.45921

Critical Value = 15.086

Decision:Reject Ho because 28.459 > 15.086

(c) Use the expected values from the Tennessee factory to perform a goodness-of-fit test with α = 0.01.

Check the assumptions:yes the assumptions are met because all expected value is greater than 5

Color	Observed	Expected	chi square contribution
Blue	30	18.67	6.875678
Orange	26	18.67	2.87782
Green	25	18.67	2.146165
Yellow	9	18.67	5.008511
Red	18	18.67	0.024044
Brown	4	18.67	11.52699
		sum	28.45921

Use the GOF-Test on your graphing calculator to find

Calculate the test statistic  = 28.45921

Critical Value = 15.086

Decision:Reject Ho because 28.459 > 15.086