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348 CHAPTER 10 STATISTICAL INFERENCE FOR TWO SAMPLES

(a) Do the data support the claim that the mean etch rate is the x 2 426 F, and s 2 3 F. Do the sample data support the claim
same for both solutions? In reaching your conclusions, use that both alloys have the same melting point? Use 0.05 and
0.05 and assume that both population variances are assume that both populations are normally distributed and have
equal. the same standard deviation. Find the P-value for the test.
(b) Calculate a P-value for the test in part (a).
10-26. Referring to the melting point experiment in
(c) Find a 95% confidence interval on the difference in mean
Exercise 10-25, suppose that the true mean difference in
etch rates.
melting points is 3 F. How large a sample would be required
(d) Construct normal probability plots for the two samples.
to detect this difference using an 0.05 level test with
Do these plots provide support for the assumptions of nor-
probability at least 0.9? Use 1 2 4 as an initial esti-
mality and equal variances? Write a practical interpreta-
mate of the common standard deviation.
tion for these plots.
10-27. Two companies manufacture a rubber material in-
10-22. Two suppliers manufacture a plastic gear used in a tended for use in an automotive application. The part will be
laser printer. The impact strength of these gears measured in subjected to abrasive wear in the field application, so we
foot-pounds is an important characteristic. A random sample decide to compare the material produced by each company in
of 10 gears from supplier 1 results in x 1 290 and s 1 12, a test. Twenty-five samples of material from each company
while another random sample of 16 gears from the second are tested in an abrasion test, and the amount of wear after
supplier results in x 2 321 and s 2 22. 1000 cycles is observed. For company 1, the sample mean and
(a) Is there evidence to support the claim that supplier 2 pro- standard deviation of wear are x 1 20 milligrams/1000
vides gears with higher mean impact strength? Use cycles and s 1 2 milligrams/1000 cycles, while for company
0.05, and assume that both populations are normally dis- 2 we obtain x 2 15 milligrams/1000 cycles and s 2 8 mil-
tributed but the variances are not equal. ligrams/1000 cycles.
(b) What is the P-value for this test? (a) Do the data support the claim that the two companies pro-
(c) Do the data support the claim that the mean impact duce material with different mean wear? Use 0.05,
strength of gears from supplier 2 is at least 25 foot-pounds and assume each population is normally distributed but
higher than that of supplier 1? Make the same assump- that their variances are not equal.
tions as in part (a).
(b) What is the P-value for this test?
10-23. Reconsider the situation in Exercise 10-22, part (a). (c) Do the data support a claim that the material from com-
Construct a confidence interval estimate for the difference in pany 1 has higher mean wear than the material from com-
mean impact strength, and explain how this interval could pany 2? Use the same assumptions as in part (a).
be used to answer the question posed regarding supplier-
to-supplier differences. 10-28. The thickness of a plastic film (in mils) on a sub-
strate material is thought to be influenced by the temperature
10-24. A photoconductor film is manufactured at a nominal at which the coating is applied. A completely randomized ex-
thickness of 25 mils. The product engineer wishes to increase periment is carried out. Eleven substrates are coated at 125 F,
the mean speed of the film, and believes that this can be resulting in a sample mean coating thickness of x 1 103.5
achieved by reducing the thickness of the film to 20 mils. and a sample standard deviation of s 1 10.2. Another 13 sub-
Eight samples of each film thickness are manufactured in a pi- strates are coated at 150 F, for which x 2 99.7 and s 2 20.1
lot production process, and the film speed (in microjoules per are observed. It was originally suspected that raising the
square inch) is measured. For the 25-mil film the sample data process temperature would reduce mean coating thickness. Do
result is x 1 1.15 and s 1 0.11, while for the 20-mil film, the data support this claim? Use 0.01 and assume that the
the data yield x 2 1.06 and s 2 0.09. Note that an increase two population standard deviations are not equal. Calculate an
in film speed would lower the value of the observation in mi- approximate P-value for this test.
crojoules per square inch.
(a) Do the data support the claim that reducing the film thick- 10-29. Reconsider the coating thickness experiment in
ness increases the mean speed of the film? Use 0.10 Exercise 10-28. How could you have answered the question
and assume that the two population variances are equal posed regarding the effect of temperature on coating thickness
and the underlying population of film speed is normally by using a confidence interval? Explain your answer.
distributed. 10-30. Reconsider the abrasive wear test in Exercise 10-27.
(b) What is the P-value for this test? Construct a confidence interval that will address the questions
(c) Find a 95% confidence interval on the difference in the in parts (a) and (c) in that exercise.
two means. 10-31. The overall distance traveled by a golf ball is tested
10-25. The melting points of two alloys used in formulating by hitting the ball with Iron Byron, a mechanical golfer with a
solder were investigated by melting 21 samples of each material. swing that is said to emulate the legendary champion, Byron
The sample mean and standard deviation for alloy 1 was Nelson. Ten randomly selected balls of two different brands
x 1 420 F and s 1 4 F, while for alloy 2 they were are tested and the overall distance measured. The data follow: