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_1^2 = sigma_2^2 versus H_1: sigma_1^2 notequalto sigma_2^2 using alpha = 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 alpha = 0.01 in answering this question.

Explanation / Answer

a) hypothesis given in question

Test Statistic = (s1^2)/(s2^2)

                          = 0.11^2 / 0.09^2

                         = 1.49382716

degree of freedom 1 = n1-1 = 8-1

                   =7

degree of freedom 2 = n2-1 = 8-1

                  =7

critical values are (0.14 & 6.99)

since Teststatistic value doe not lie in rejection region ,we fail to reject the null hypothesis

b) Test statistic = 1.5^2 = 2.25    ( 50% larger than other sd ---> which gives 1.5^2)( 1.5s^2/s^2 =1.5^2)

   critical value for = 0.01      are 0.11 and 8.89

since Test statistic does not lie in rejection region ,we fail to reject the null hypothesis.

hence  the sample size n1 = n2 = 8 is not adequate to detect this difference with high probability

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