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Comparing Plastic Gear Strengths: Supplier 1 vs. Supplier 2 Analysis
Chapter 10, Problem 24E(choose chapter or problem)
Two suppliers manufacture a plastic gear used in a laser printer. The impact strength of these gears measured in foot-pounds is an important characteristic. A random sample of 10 gears from supplier 1 results in \(\bar{x}_{1}=290\) and \(s_{1}=12\), and another random sample of 16 gears from the second supplier results in \(\bar{x}_{2}=321\) and \(s_{2}=22\).
(a) Is there evidence to support the claim that supplier 2 provides gears with higher mean impact strength? Use \(\alpha=0.05\), and assume that both populations are normally distributed but the variances are not equal. What is the P-value for this test?
(b) Do the data support the claim that the mean impact strength of gears from supplier 2 is at least 25 foot-pounds higher than that of supplier 1? Make the same assumptions as in part (a).
(c) Construct a confidence interval estimate for the difference in mean impact strength, and explain how this interval could be used to answer the question posed regarding supplier-to-supplier differences.
Questions & Answers
QUESTION:
Two suppliers manufacture a plastic gear used in a laser printer. The impact strength of these gears measured in foot-pounds is an important characteristic. A random sample of 10 gears from supplier 1 results in \(\bar{x}_{1}=290\) and \(s_{1}=12\), and another random sample of 16 gears from the second supplier results in \(\bar{x}_{2}=321\) and \(s_{2}=22\).
(a) Is there evidence to support the claim that supplier 2 provides gears with higher mean impact strength? Use \(\alpha=0.05\), and assume that both populations are normally distributed but the variances are not equal. What is the P-value for this test?
(b) Do the data support the claim that the mean impact strength of gears from supplier 2 is at least 25 foot-pounds higher than that of supplier 1? Make the same assumptions as in part (a).
(c) Construct a confidence interval estimate for the difference in mean impact strength, and explain how this interval could be used to answer the question posed regarding supplier-to-supplier differences.
ANSWER:Step 1 of 8
Given,
\( {{n}_{1}}=10 \\ \)
\({{{\bar{x}}}_{1}}=290 \\ \)
\( {{s}_{1}}=12 \\ \)
\( {{n}_{2}}=16 \\ \)
\( {{{\bar{x}}}_{2}}=321 \\ \)
\( {{s}_{2}}=22 \\ \)
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Comparing Plastic Gear Strengths: Supplier 1 vs. Supplier 2 Analysis
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This video presents a comparison between two suppliers of plastic gears in terms of their mean impact strength. Using statistical tools like the two-sample t-test and confidence intervals, we evaluate which supplier offers stronger gears.