Formulate an appropriate hypothesis test

Question

Discussion:

Q: A manufacturer is interested in determining whether it can claim that the boxes of detergent it sells contain, on average, more than 500 grams of detergent. From past experience the manufacturer knows that the amount of detergent in the boxes is approximately normally distributed. The firm selects a random sample of 100 boxes and records the amount of detergent (in grams) in each box. Formulate an appropriate hypothesis test and report a p-value. Do you find statistical support for the manufacturer's claim? Explain.

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