A study is performed in a large southern town to determine whether the average amount spent on food per four-person family in the town is significantly different from the national average. A random sample of the weekly grocery bills of two-person families in this town is given in the file. Assume the national average amount spent on food for a four-person family is $150. a. Identify the null and alternative hypotheses for this situation.
b. Is the sample evidence statistically significant? If so, at what significance levels can you reject the null hypothesis?
c. For which values of the sample mean (e. g., average weekly grocery bill) would you reject the null hypothesis at the 1% significance level? For which values of the sample mean would you reject the null hypothesis at the 10% level?
FamilyWeekly food expense
1 $198.23
2 $143.53
3 $207.48
4 $134.55
5 $182.01
6 $189.84
7 $170.36
8 $163.72
9 $155.73
10 $203.73
11 $191.19
12 $172.66
13 $154.25
14 $179.03
15 $130.29
16 $170.73
17 $194.50
18 $171.14
19 $175.19
20 $177.25
21 $166.62
22 $135.54
23 $141.18
24 $158.48
25 $159.78
26 $157.42
27 $98.40
28 $181.63
29 $128.45
30 $190.84
31 $154.04
32 $190.22
33 $161.48
34 $113.42
35 $148.83
36 $197.68
37 $135.49
38 $146.72
39 $176.62
40 $154.60
41 $178.39
42 $186.32
43 $157.94
44 $116.35
45 $136.81
46 $195.58
47 $129.44
48 $146.84
49 $165.63
50 $158.97
51 $210.00
52 $175.46
53 $159.69
54 $154.56
55 $152.95
56 $177.30
57 $129.23
58 $127.40
59 $167.48
60 $183.83
61 $157.39
62 $163.24
63 $165.01
64 $137.43
65 $177.37
66 $142.68
67 $150.04
68 $161.44
69 $166.13
70 $190.96
71 $187.19
72 $116.63
73 $159.73
74 $159.64
75 $142.44
76 $153.03
77 $143.12
78 $156.35
79 $182.70
80 $129.03
81 $119.06
82 $137.99
83 $144.20
84 $183.51
85 $169.67
86 $134.66
87 $202.94
88 $143.43
89 $170.52
90 $139.53
91 $159.31
92 $134.77
93 $165.48
94 $127.20
95 $168.16
96 $125.39
97 $167.96
98 $178.64
99 $134.38
100 $111.87