Amount of Detergent in Random Sample
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A manufacturer is interested in determining whether a claim that boxes of detergent it sells contain on average, more than 500 grams of detergent. From past experience the manufacturer assumes that the amount of detergent in the boxes is normally distributed. The firm takes a random sample of 100 boxes and records the amount of detergent (in grams) in each box.
Based on the data in the attached file, is it still reasonable for the manufacturer to assume that the amount of detergent in these boxes is normally distributed? Perform a chi-square goodness-of-fit test. Report and interpret the computed p-value.
Amount of Detergent in Randomly Selected Boxes of Detergent
Box Amount
1 454.54
2 624.83
3 590.83
4 489.21
5 451.17
6 587.00
7 691.45
8 639.36
9 566.83
10 398.53
11 491.43
12 564.74
13 492.30
14 403.60
15 569.00
16 499.95
17 501.19
18 408.54
19 409.48
20 536.08
21 525.91
22 622.91
23 484.38
24 531.88
25 677.56
26 437.61
27 574.11
28 425.42
29 417.39
30 448.59
31 609.73
32 485.50
33 408.87
34 646.30
35 533.23
36 473.36
37 527.50
38 558.64
39 480.63
40 531.41
41 470.53
42 675.10
43 513.33
44 531.92
45 561.41
46 570.61
47 572.58
48 688.70
49 652.79
50 590.96
51 527.44
52 531.17
53 482.93
54 691.13
55 559.99
56 566.67
57 687.72
58 585.02
59 559.95
60 423.32
61 504.87
62 523.31
63 545.58
64 521.31
65 471.16
66 600.68
67 466.97
68 615.45
69 553.24
70 450.54
71 460.37
72 592.05
73 550.87
74 420.84
75 426.61
76 488.35
77 413.97
78 467.98
79 483.21
80 452.91
81 483.77
82 422.81
83 627.47
84 508.39
85 569.39
86 409.81
87 509.94
88 620.98
89 493.66
90 484.60
91 684.94
92 497.19
93 469.03
94 496.13
95 474.51
96 492.15
97 506.46
98 466.49
99 496.91
100 497.52
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Solution Summary
This solution looks at the normal distribution of the amount of detergent in boxes. A null and alternative hypothesis is provided and a chi-square goodness-of-fit test is conducted.
Solution Preview
Please see the attached file.
Hypothesis: H0: m = 500 grams vs. HA: m > 500 grams
Level of Significance: a = 5%
Decision Rule: Reject the null ...
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