Suppose that thickness of a part used in semiconductor is its critical dimension

Question

Suppose that thickness of a part used in semiconductor is its critical dimension and that measurements of the thickness of a random sample of 18 such parts have the variance s^2 = 0.68, where the measurements are in thousandths of an inch. The process is considered to be under control if the variation of the thicknesses is given by a variance not greater than 0.36. Assuming that the measurement constitute a random sample from a normal population, test the null hypothesis sigma^2 = 0.36 against the alternative hypothesis sigma^2 > 0.36 at the 0.05 level of significance. (Reference X_0.05 (17)) = 27.587) 10.1. Find the line of regression of Y on X for the data of

Explanation / Answer

Null Hypothesis: s^2 = 0.36

Alternative Hypothesis: s^2 > 0.36

Level of significance is 0.05

Test Statistics:

X^2 = ((n-1)*s1^2)/s^2

        = ((18-1)*0.68)/0.36

        = 32.111

Critical chi-square value is 27.585

The calculated test statistics is greater than the critical value (32.111 > 27.585); we fail to reject the null hypothesis.

At 5% level of significance there is not sufficient evidence to conclude that the s^2 (population standard deviation) is greater than 0.36.

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