8-6 p421 n06
Original claim: the standard deviation less than or equal to 15
σ ≤ 15

The Null Hypothesis
H₀: σ = 15

The Alternate Hypothesis
H₁: σ > 15

A sample of n = 5 has 4 degrees of freedom.
For a right tailed test and a level of significance, α = 0.05
χ²_critical = 9.488

Data:
s = 30
χ²_test = (5-1)×30² ⁄ 15² = 16

Because 16 is IN the Critical Region, we Reject the Null Hypothesis and the statistical analysis of the data can reject the original claim.

Conclusion:
There is sufficient evidence to warrant rejection of the claim that the standard deviation less than or equal to 15