Question

Eleven resilient modulus observations of a ceramic mixture of type A are measured and found to have a sample average of 18.42 psi and sample standard deviation of 2.77 psi. Ten resilient modulus observations of a ceramic mixture of type B are measured and found to have a sample average of 19.28 psi and sample standard deviation of 2.41 psi. (a) Is there sufficient evidence to support the claim that type A ceramic has larger variability than type B? Use a = 0.05. (b) Compute the appropriate 95% confidence interval corresponding to your test in part (a).

Answer 1

a)

H:01 = 022

   

H: 012 > 022

The test statistic F = $\frac{s1^2}{s2^2}$

                              = (2.77)^2/(2.41)^2

                              = 1.32

At alpha = 0.05, the critical value is F(0.05, 10, 9) = 3.1373

Since the test statistic value is not greater than the critical value, so we should not reject the null hypothesis

At 0.05 significance level, there is not sufficient evidence to support the claim that type A ceramic has larger variability than type B.

b) At 95% confidence level, the critical values are

F_L = F(0.975, 10, 9) = 0.2646

F_R = F(0.025, 10, 9) = 3.9639

The 90% confidence interval for $\frac{\sigma1^2}{\sigma2^2}$ is

$1? 1 $22 * FR 0 -22 s1 1 -22 * Fy

_ (2.77) 1 (2.4152*3.9639* (2.77) 1 23*2.4152*0.2646

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