A new filtering device is installed in a chemical unit. Before its installation,

Question

A new filtering device is installed in a chemical unit. Before its installation, a random sample yielded the following information about the percentage of impurity y bar _1 = 12.5, s^2 _1 = 101.17, and n = 8. After installation, a random sample yielded y bar _ 2 = 10.2, s_2^2 = 94.73, and m = 9 (a) Can you concluded that the two variances are equal? Use alpha = .05. (b) Has the filtering device reduced the percentage of impurity significantly? Use alpha =.05. (c) Find a 95 percent confidence interval on the difference in the percentages of impurities.

Explanation / Answer

a)

F = s12   / S22   = 1.068

The critical value of Fcric( 0.05,7,8) =3.50

Since the calculated value 1.068 is less than 3.50, hence we accept null hypothesis and conclude that variance are equal.

b)

The critical value at 17 degrees of freedom with 0.05 level of significance is 2.110

Since the calculated value is 0.478, which is less than the critical value 2.110, hence we accept the null hypothesis and conclude that The filtering device has not reduced the percentage of impurity significantly.

n1= 8 n2 = 9 Ybar   = 12.5 Xbar   = 10.2 s1 = 10.05833 S2 = 9.732934 s12 = 101.17                      S22=                94.73

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