Answer:
Step-by-step explanation:
For the sample, n = 12
Mean, x = (158.2 + 162.8 + 161.5 + 161.2 + 166.5 + 160.1 + 158.4 + 175.6 + 159.9 + 168.8 + 161.9 + 163.7)/12 = 163.22
Variance, s² = (summation(x - mean)²/n
Summation(x - mean)² = (158.2 - 163.22)^2 + (162.8 - 163.22)^2 + (161.5 - 163.22)^2 + (161.2 - 163.22)^2+ (166.5 - 163.22)^2 + (160.1 - 163.22)^2 + (158.4 - 163.22)^2 + (175.6 - 163.22)^2 + (159.9 - 163.22)^2 + (168.8 - 163.22)^2 + (161.9 - 163.22)^2 + (163.7 - 163.22)^2 = 273.5368
Variance, s² = 273.5368/12 = 22.79
This is a test for a single variance. We would set up the test hypothesis.
For the null hypothesis,
H0: σ² ≥ 25
For the alternative hypothesis,
H1: σ² < 25
The formula for determining the test statistic,x² is
x² = (n - 1)s²/σ²
Where n - 1 is the degree of freedom, df.
df = 12 - 1 = 11
x² = (11 × 22.79)/25 = 10.0276
For a test of 90% reliability, Confidence level = 0.9
Cl = 1 - alpha(level of significance)
alpha = 1 - 0.9 = 0.1
The critical value from the chi-square distribution table is 17.28. Since 17.28 > 10.0276, we would reject the null hypothesis. Therefore, the filling machine does not need repair because the variance of the process is not more than 25 oz.
