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An automotive part must be machined to close tolerances to be acceptable to customers. Production specifications call for a maximum variance in the lengths of the parts of .00041. Suppose the sample variance for 27 parts turns out to be s2 = .00063. Using α = .05, conduct an appropriate hypothesis test to determine whether the population variance specification is being violated. Use the p‐value approach and 5‐step procedure discussed in class.

Step 1: Hypothesis:
H0: σ2 = 0.00041
H1: σ2> 0.00041
Step 2: Calculate test statistic
χ2 = (n-1)*s2/σ2
= (27-1)*0.00063/0.00041
= 39.95
Step 3: For α = 0.05 and df = n-1 = 26 , Critical χ2 = 38.885, (value taken from chi-square table)
Step 4: At 5% significance level, test statistic (39.95) falls into the rejection region, therefore, null hypothesis is rejected.
 
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