Question

•Two pharmaceutical machines are used for filling antiseptic ointment in a glass tube with a net volume of 5 ml. The fill volume can be assumed normal, with standard deviation ?1=0.01 and ?2=0.015 ounces. A member of the quality engineering staff suspects that both machines fill the same mean net volume, whether or not this volume is 5 ml. A random sample of 10 bottles is taken from each machine with ?1=5.02 ml and ?2=4.97 ml

a. Do you think the engineer is correct? ? =0.05 ; Use Zo approach

b.Use the P-value approach

c.Find a 95% CI on the differences in means. Provide practical implementation of this interval

Answer 1

a) H₀:

    H₁:

The test statistic z = ()/

                              = (5.02 - 4.97)/sqrt((0.01)^2/10 + (0.015)^2/10)

                              = 8.77

At alpha = 0.05, the critical values are +/- z_0.025 = +/- 1.96

Since the test statistic value is greater than the critical value(8.77 > 1.96), so we should reject H₀.

There is not sufficient evidence to support the engineer's claim.

b) P-value = 2 * P(Z > 8.77)

                 = 2 * (1 - P(Z < 8.77))

                 = 2 * (1 - 1)

                 = 2 * 0 = 0

c) At 95% confidence interval the critical value is z^* = 1.96

The 95% confidence interval is

() +/- z^* *

= (5.02 - 4.97) +/- 1.96 * sqrt((0.01)^2/10 + (0.015)^2/10)

= 0.05 +/- 0.0112

= 0.0388, 0.0612

We are 95% confident that the true difference in population means lies within the confidence bounds 0.0388 and 0.0612