Hypothesis Testing of Mean: Bottling plant filling process

See attached file with data set.

Decision of Uncertainty

PLEASE SHOW ALL WORK

You are the quality manager for a bottling plant. If the filling process is working as intended,
cans stamped with 12 oz. will be filled with just over 12 oz. of liquid. On average, the plant
owners want 12.25 oz. in each can.

The data below represent a random selection of cans bottled during the previous shift.

Can Ounces
1 12.740
2 12.545
3 12.849
4 12.270
5 12.320
6 12.460
7 12.363
8 12.753
9 12.260
10 12.583
11 12.662
12 12.462
13 12.431
14 12.605
15 12.645
16 12.376
17 12.686
18 12.719
19 12.827
20 12.727
21 12.735
22 12.726
23 12.310
24 12.783
25 12.763
26 12.697
27 12.320
28 12.973
29 12.340
30 12.669
31 12.420
32 12.478
33 12.908
34 12.980
35 12.470
36 12.783
37 12.695
38 12.935
39 12.724
40 12.952
41 12.511
42 12.631
43 12.496
44 12.727
45 12.794
46 12.806
47 12.736
48 12.380
49 12.452
50 12.653
51 12.285
52 12.120
53 12.544
54 12.669
55 12.952
56 12.893
57 12.975
58 12.919
59 12.526
60 12.577
61 12.939
62 12.865
63 12.612
64 12.752
65 12.826
66 12.912
67 12.828
68 12.618
69 12.310
70 12.897
71 12.814
72 12.966
73 12.972
74 12.673
75 12.615
76 12.160
77 12.560
78 12.488
79 12.942
80 12.928
81 12.150
82 12.200
83 12.600
84 12.823
85 12.800
86 12.891
87 12.795
88 12.589
89 12.445
90 12.966
91 12.889
92 12.924
93 12.843
94 12.595
95 12.340
96 12.738
97 12.632
98 12.636
99 12.714

Complete the following:

a What is the population of interest?

b What are the null and alternate hypotheses?

c What is the decision rule?

d At 95% confidence, is the bottling process working as intended? Discuss your findings in
detail. (Remember, this is a business. Your findings should be presented in statistical terms
with a conclusion that your manager can understand.)