Pull-strength tests on a set of 10 soldered leads for a semiconductor device yie

Question

Pull-strength tests on a set of 10 soldered leads for a semiconductor device yielded a variance of S12 = 10.441. Another set of 8 soldered leads were tested after an encapsulation was applied; these tests yielded a variance of S22 = 1.8455. Quality controllers are hopeful that the encapsulation process significantly reduces the variance, making for a product with more reliably reproducible specifications. Does the evidence suggest that encapsulation produces a significantly reduced variance in pull strengths? [Hint: Assume that the population variance for soldered leads without encapsulation is the same as the population variance for soldered leads with encapsulation; then evaluate the probability of observing the sample variances as unusually or more unusually related as those observed.]

Explanation / Answer

Let X = Pull-strength for soldered leads without encapsulation

      Y = Pull-strength for soldered leads with encapsulation

Let Population variance, V(X) = 12 and V(Y) = 22

Claim: The encapsulation process significantly reduces the variance, i.e., 22 < 12

Hypotheses:

Null H0: 12 = 22   Vs Alternative HA: 12 > 22

Test statistic:

F = s12/s22 where s1 and s2 are standard deviations based on n1 observations on X and n2 observations on Y.

Calculations

Given s1 = 10.441 and s2 = 1.8455, Fcal = 5.658

Distribution, Critical Value and p-value

Under H0, F ~ Fn1 – 1, n2 – 1

p-value = P(Fn1 – 1, n2 – 1 > F(cal)) = P(F9, 7 > 5.658) = 0.0115

Decision:

Since p-value is low, just about 1%, H0 is rejected.

Conclusion:

There is sufficient evidence to support the claim that the encapsulation process significantly reduces the variance.

DONE

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