8-6 p422 n12
Original claim: the new production line has errors with a standard deviation different from 43.7
σ ≠ 43.7

The Null Hypothesis
H₀: σ = 43.7

The Alternate Hypothesis
H₁: σ ≠ 43.7

A sample of n = 81 has 80 degrees of freedom.
For a two tailed test and a level of significance, α = 0.05
χ²_critical = 57.153 and 106.629

Data:
s = 52.3
χ²_test = (81-1)×52.3² ⁄ 43.7² = 114.586

Because 114.586 is IN the Critical Region, we Reject the Null Hypothesis and the statistical analysis of the data can support the original claim.

Conclusion:
The sample data SUPPORT the claim that the new production line has errors with a standard deviation different from 43.7