This question is incomplete, the complete question is;
A rivet is to be inserted into a hole. A random sample of n = 15 parts is selected and the hole diameter is measured. The sample standard deviation is s = 0.008 millimeters. Is there strong evidence to indicate that the standard deviation of hole diameter exceeds 0.01 millimeters, Use ∝ = 0.01
Answer:
since our test statistics ( 8.96 ) is less than the critical value ( 29.141 ),
there is no strong evidence to indicate that the standard deviation of hole diameter exceeds 0.01 millimeters.
Step-by-step explanation:
Given that;
H₀ : σ = 0.01
H₁ : σ > 0.01
The test statistics is;
X² = ( n-1 )s² / σ² = ( 15 - 1)(0.008)² / (0.01)²
= 0.000896 / 0.0001
= 8.96
degree of freedom
df = n - 1 = 15 - 1 = 14
For right tailed test, critical value at 0.01 level of significance is 29.141.
Now since our test statistics ( 8.96 ) is less than the critical value ( 29.141 ),
there is no strong evidence to indicate that the standard deviation of hole diameter exceeds 0.01 millimeters.
