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Patent infringement case. Chance (Fall 2002) described a
Chapter 8, Problem 19E(choose chapter or problem)
Patent infringement case. Chance (Fall 2002) described a lawsuit charging Intel Corp. with infringing on a patent for an invention used in the automatic manufacture of computer chips. In response, Intel accused the inventor of adding material to his patent notebook after the patent was witnessed and granted. The case rested on whether a patent witness’s signature was written on top of or under key text in the notebook. Intel hired a physicist who used an X-ray beam to measure the relative concentrations of certain elements (e.g., nickel, zinc, potassium) at several spots on the notebook page. The zinc measurements for three notebook locations—on a text line, on a witness line, and on the intersection of the witness and text line—are provided in the following table and saved in the PATENT file.
a. Use a test or a confidence interval (at \(\alpha\ =\ .05\) ) to compare the mean zinc measurement for the text line with the mean for the intersection.
b. Use a test or a confidence interval (at \(\alpha\ =\ .05\) ) to compare the mean zinc measurement for the witness line with the mean for the intersection.
c. From the results you obtained in parts a and b, what can you infer about the mean zinc measurements at the three notebook locations?
d. What assumptions are required for the inferences to be valid? Are they reasonably satisfied?
Questions & Answers
QUESTION:
Patent infringement case. Chance (Fall 2002) described a lawsuit charging Intel Corp. with infringing on a patent for an invention used in the automatic manufacture of computer chips. In response, Intel accused the inventor of adding material to his patent notebook after the patent was witnessed and granted. The case rested on whether a patent witness’s signature was written on top of or under key text in the notebook. Intel hired a physicist who used an X-ray beam to measure the relative concentrations of certain elements (e.g., nickel, zinc, potassium) at several spots on the notebook page. The zinc measurements for three notebook locations—on a text line, on a witness line, and on the intersection of the witness and text line—are provided in the following table and saved in the PATENT file.
a. Use a test or a confidence interval (at \(\alpha\ =\ .05\) ) to compare the mean zinc measurement for the text line with the mean for the intersection.
b. Use a test or a confidence interval (at \(\alpha\ =\ .05\) ) to compare the mean zinc measurement for the witness line with the mean for the intersection.
c. From the results you obtained in parts a and b, what can you infer about the mean zinc measurements at the three notebook locations?
d. What assumptions are required for the inferences to be valid? Are they reasonably satisfied?
ANSWER:Solution:
Step 1 of 4:
Given the zinc measurements for three notebook locations on a text line, on a witness line, and on the intersection of the witness and text line are provided in the given table.
Text line |
0.335 |
0.374 |
0.440 |
|||
Witness line |
0.210 |
0.262 |
0.188 |
0.329 |
0.439 |
0.397 |
Intersection |
0.393 |
0.353 |
0.285 |
0.295 |
0.319 |
a). To use a test or a confidence interval (at to compare the mean zinc measurement for the text line with the mean for the intersection.
Let mean zinc measurement for the text-line,
mean zinc measurement for the witness-line,
mean zinc measurement for the intersection.
Then,
= 0.0022
For ,
Degrees of freedom
= 3+5 - 2
= 6
Then the critical value is
(this value from critical values of the t- distribution)
Now, the 95% confidence interval is
0.0540.0848
(- 0.0308, 0.1388)
We are 95% confident that the difference in the mean zinc level between text-line and intersection is between -0.0308 and 0.1388.
To determine if there is a different in the mean zinc measurement between text-line and intersection.
The test statistic is
= 1.56
The rejection region requires in each tail of t-distribution with
= 3 + 5 - 2
= 6
Then the critical value is
(this value from critical values of the t- distribution)
Now the rejection region is
Since the observed value of the test statistic does not fall in the rejection region
( t = 1.56 < 2.447). So is not rejected.
Conclusion:
Therefore, there is insufficient evidence to indicate a difference in the mean zinc measurement between text -line and intersection at .