A photoconductor film is manufactured at a nominal thickness of 25 mils. The pro

Question

A photoconductor film is manufactured at a nominal thickness of 25 mils. The product engineer wishes to increase the mean speed of the film and believes that this can be achieved by reducing the thickness of the film to 20 mils. Eight samples of each film thickness are manufactured in a pilot production process, and the film speed (in microjoules per square inch) is measured. For the 25-mil film, the sample data result is s_1 = 0.11, and for the 20-mil film the data yield s_2 = 0.09. a) Test H_0: sigma^2_1 = sigma^2_2 versus H_1: sigma^2_1 notequalto sigma^2_2 using sigma = 0.02. (b) Suppose that one population standard deviation is 50% larger than the other. Is the sample size n1 = n2 = 8 adequate to detect this difference with high probability? Use sigma = 0.01 in answering this question.

Explanation / Answer

f = s1^2 / s2^2

= (0.11^2 /0.09^2) = 1.493827

df1= n1 -1 = 7

df2= 7

F-critical value = 0.14 and 6.99

since TS is not in rejection region ,we fail to reject the null

b) if TS = s1^2 / s2^2 = 1.5^2 =  2.25

f-critical = 0.11, 8.89

since 0.11 < 2.25 < 8.89

we fail to reject the null

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