Problem:
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 given below, 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