A soda machine is set to fill bottles with 24 ounces of cola. As part of a quality control program, an inspector records the amount of fill over or under 24 ounces for one minute. His observations are shown below.
| -0.40 | -0.45 | -0.21 | -0.15 | -0.71 | -0.05 | -0.84 | -0.12 | -0.05 | -0.58 |
| -0.55 | -1.01 | -0.07 | 0.50 | 0.08 | -0.96 | -0.36 | -0.75 | -0.84 | -1.00 |
| 0.21 | 0.25 | 0.10 | 0.99 | 0.89 | 0.05 | 0.54 | 0.31 | 0.97 | 0.67 |
| 0.45 | 0.60 | 0.01 | 0.98 | 0.22 | 0.72 | 0.77 | 0.48 | 0.13 | 0.39 |
| -0.73 | -0.78 | -0.90 | -0.14 | -0.68 | 0.80 | 0.12 | 0.16 | 0.37 | 0.27 |
Is there evidence at the α = 0.01 level of significance to support the hypothesis that the filling process is not random with respect to amounts over and under 24 ounces?
◦ z = -6.28
Since |z| > z
0.005 = 2.58, we reject H
0. There is sufficient evidence to support the hypothesis that the filling process is not random.
◦ z = 0.67
Since |z| < z
0.005 = 2.58, we do not reject H
0. There is not sufficient evidence to support the hypothesis that the filling process is not random.
◦ z = -5.71
Since |z| > z
0.005 = 2.58, we reject H
0. There is sufficient evidence to support the hypothesis that the filling process is not random.
◦ z = -1.25
Since |z| < z
0.005 = 2.58, we do not reject H
0. There is not sufficient evidence to support the hypothesis that the filling process is not random.
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