Question

A sample of 15 consumers provided the following product ratings for three different products. Five consumers were randomly assigned to test and rate each product.

Product | ||
---|---|---|

A | B | C |

58 | 88 | 68 |

61 | 97 | 47 |

77 | 96 | 38 |

46 | 89 | 56 |

67 | 98 | 59 |

Use the Kruskal-Wallis test and *α* = 0.05 to determine
whether there is a significant difference among the ratings for the
products.

a) Find the value of the test statistic.

b) Find the *p*-value. (Round your answer to three
decimal places.)

*p*-value =

State your conclusion.

Answer #1

Type | score | Rank |

A | 58 | 5 |

A | 61 | 7 |

A | 77 | 10 |

A | 46 | 2 |

A | 67 | 8 |

B | 88 | 11 |

B | 97 | 14 |

B | 96 | 13 |

B | 89 | 12 |

B | 98 | 15 |

C | 68 | 9 |

C | 47 | 3 |

C | 38 | 1 |

C | 56 | 4 |

C | 59 | 6 |

sample size n_{i} |
sum of ranks ∑R_{i} |
(∑R_{i})^{2}/n_{i} |
|||

A | 5 | 32 | 204.80 | ||

B | 5 | 65 | 845.00 | ||

C | 5 | 23 | 105.80 | ||

total N = | 15 | total = |
∑(∑R_{i})^{2}/n_{i} = |
1155.60 | |

test stast:H= |
=(12/(N*(N+1)))*∑(∑Ri)^{2}/ni )-3*(N+1)= |
9.780 |

**a)**

**value of the test statistic =9.78**

**b)**

**p value =0.008**

reject null hypothesis since p value <0.05

A sample of 15 consumers provided the following product ratings
for three different products. Five consumers were randomly assigned
to test and rate each product.
Product
A
B
C
56
86
66
62
93
43
73
91
36
41
88
51
63
96
58
Use the Kruskal-Wallis test and α = 0.05 to determine
whether there is a significant difference among the ratings for the
products.
Find the value of the test statistic._____
Find the p-value. (Round your answer to...

Question 9-15 are based on the random
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about the population mean. Test the hypothesis that the mean is
less than 80.
80
100
81
93
80
57
98
90
71
56
58
78
59
55
55
77
72
78
56
94
98
59
93
86
89
62
60
66
59
71
96
97
94
69
64
77
87
77
64
90
90
95
98
99
56
69
72
81
95...

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You may need to use the appropriate technology to answer this
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A sample of 15 consumers provided the following product ratings
for three different products. Five consumers were randomly assigned
to test and rate each product.
Product
A
B
C
57
87
67
66
99
49
79
93
37
43
81
53
69
97
51
Use the Kruskal-Wallis test and α = 0.05 to determine
whether there is a significant difference among the ratings for the
products.
State the...

Student Grades
Student
Test
Grade
1
76
62
2
84
90
3
79
68
4
88
84
5
76
58
6
66
79
7
75
73
8
94
93
9
66
65
10
92
86
11
80
53
12
87
83
13
86
49
14
63
72
15
92
87
16
75
89
17
69
81
18
92
94
19
79
78
20
60
71
21
68
84
22
71
74
23
61
74
24
68
54
25
76
97...

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Sample
Satisfaction Rating
Repair Requests
1
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13...

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Class 1
Class 2
Class 3
Class 4
95
79
77
81
99
68
91
96
75
84
84
68
76
78
84
89
82
74
75
78
97
93
82
75
93
95
82
88
83
88
85
98
86
95
96
59
What conclusion can we make about the hypothesis test?

Consumers Union provides ratings on a large variety of consumer
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One recent article rated laundry detergents on a scale from 1 to
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Rating
Price (cents)
61
18
55
30
48
16
46
13
35
8
32
5
59
22
52
23
47
15
46...

Below represent scores on an exam, each entry one score for one
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40
99
59
98
63
63
64
65
67
35
67
67
68
70
71
71
71
46
72
72
60
73
74
74
74
75
97
75
62
76
76
76
76
76
77
57
77
98
77
63
78
78
78
79
79
80
80
80
80
80
81
81
92
81
93
82
82
83
83
83
83
83
83
83
84
84
84...

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Rating
Price (cents)
59
18
55
30
48
16
46
13
35
8
32
5
59
22
52
23
47
15
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