Question

- Is there enough evidence that the average number of PURPLE Skittles in a package is greater than the average number of ORANGE Skittles in a package? Use the attached Skittles sample and test at the significance level of .01

Package | Red | Orange | Yellow | Green | Purple | Total | Dominant Color |

1 | 15 | 15 | 16 | 12 | 14 | 72 | Y |

2 | 13 | 6 | 11 | 16 | 15 | 61 | G |

3 | 9 | 9 | 10 | 18 | 15 | 61 | G |

4 | 7 | 9 | 8 | 18 | 15 | 57 | G |

5 | 13 | 9 | 14 | 10 | 7 | 53 | Y |

6 | 15 | 20 | 8 | 10 | 9 | 62 | O |

7 | 12 | 11 | 11 | 16 | 8 | 58 | G |

8 | 14 | 14 | 15 | 5 | 12 | 60 | Y |

9 | 14 | 14 | 15 | 5 | 12 | 60 | Y |

10 | 16 | 10 | 13 | 10 | 10 | 59 | R |

11 | 14 | 11 | 12 | 13 | 9 | 59 | R |

12 | 10 | 11 | 16 | 8 | 15 | 60 | Y |

13 | 7 | 15 | 12 | 12 | 13 | 59 | O |

14 | 7 | 15 | 12 | 12 | 13 | 59 | O |

15 | 18 | 10 | 10 | 9 | 13 | 60 | R |

16 | 10 | 9 | 12 | 15 | 9 | 55 | G |

17 | 8 | 13 | 11 | 6 | 21 | 59 | P |

18 | 12 | 14 | 12 | 10 | 11 | 59 | O |

19 | 12 | 8 | 11 | 15 | 12 | 58 | G |

20 | 14 | 5 | 13 | 14 | 13 | 59 | R |

21 | 16 | 10 | 11 | 15 | 10 | 62 | R |

22 | 10 | 9 | 9 | 9 | 21 | 58 | P |

23 | 15 | 6 | 12 | 12 | 12 | 57 | R |

24 | 10 | 12 | 17 | 9 | 8 | 56 | Y |

25 | 16 | 7 | 16 | 10 | 11 | 60 | R |

26 | 12 | 10 | 12 | 8 | 16 | 58 | P |

27 | 7 | 13 | 5 | 11 | 15 | 51 | P |

28 | 8 | 11 | 18 | 12 | 11 | 60 | Y |

29 | 14 | 9 | 10 | 11 | 13 | 57 | R |

30 | 12 | 12 | 12 | 7 | 14 | 57 | P |

31 | 16 | 7 | 10 | 7 | 13 | 53 | R |

32 | 13 | 14 | 13 | 7 | 12 | 59 | O |

33 | 10 | 9 | 9 | 9 | 21 | 58 | P |

34 | 13 | 7 | 14 | 14 | 10 | 58 | Y |

35 | 11 | 9 | 19 | 6 | 13 | 58 | Y |

36 | 10 | 11 | 14 | 12 | 10 | 57 | Y |

37 | 11 | 9 | 19 | 6 | 13 | 58 | Y |

38 | 8 | 13 | 15 | 14 | 9 | 59 | Y |

39 | 14 | 13 | 13 | 6 | 11 | 57 | R |

40 | 12 | 10 | 14 | 6 | 11 | 53 | Y |

41 | 8 | 11 | 15 | 14 | 12 | 60 | Y |

Answer #1

Here we use two sample t test to test :

Test results from MINITAB :

Two-Sample T-Test and CI: Purple, Orange

Two-sample T for Purple vs Orange

N Mean StDev SE Mean

Purple 41 12.49 3.26 0.51

Orange 41 10.73 3.02 0.47

Difference = mu (Purple) - mu (Orange)

Estimate for difference: 1.756

99% lower bound for difference: 0.110

T-Test of difference = 0 (vs >): T-Value = 2.53 P-Value = 0.007
DF = 80

Both use Pooled StDev = 3.1391

as p value = 0.007 < 0.01 , we reject the null hypothesis .

Or in other words , average number of purple skittles are greater than average number of orange skittles

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Bag
Blue
Orange
Green
Yellow
Red
Brown
Total Number of Candies
1
7
23
9
11
4
6
60
2
16
16
4
7
9
4
56
3
14
14
3
10
5
11
57
4
13
14
7
8
8
6
56
5
18
12
7
10
5
7
59
6
12
9
11
9
8
8
57
7
15
16
6
6
6
8
57
8
15
17
8
4
6
7
57
9
12
14
10
5...

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11 12 15 16 13 18 16 17 12 12 14 9 11 14 19 13 11 17 11 13 15 14 18
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14
17
17
6
8
17
21
16
6
17
11
17
15
16
20
19
6
12
17
22
20
17
11
11
9
22
17
18
21
20
26
7
16
19
18
11
21
17
25
16
22
14
14
16
18
20
21
11
19
13
6
11
19
14
18
31
13
15
17
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y
1
12
60
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16
87
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18
91
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10
50
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17
94
6
11
62
7
14
67
8
13
64
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y
1
2.0
3
23.33
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65.33
4
12.65
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50
6
60
7
16
8
32.6
10
87.9
9
99.8
21
54.7
11
21.9
13
55.7
14
21.6
15
67.7
16
76.8
17
12.8
18
52.7
18
12.8
16
27.9
15
87.8
80
22.3
54
54.7
54
12.65
21
76.7
42
121
65
65
22
364.66
21
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