About This Assignment

This mini-project covers interval estimation, which is developed in chapter 7 of MS. You will be tasked with answering a challenging word problem. You will be asked to show your work on the next assignment page by submitting HTML.

Format: numeric answer "quiz"
Time limit: none
Number of attempts: 3 total

Academic Integrity

Getting help from your peers is not permitted.
Collaborating, or completing the quiz with others in the class, is not permitted.
Copying or reusing previous work is not permitted.
Open-book research for the quiz is permitted and encouraged.

A patent problem

Introduction

(From MS 7.44). Patent infringement case. Chance (Fall 2002) described a lawsuit where Intel Corp. was charged 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 key text in the notebook or under the key text. Intel hired a physicist who used an X-ray beam to measure the relative concentration 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 lines—are provided in the table.

The data is also contained in this PATENT Excel file.

zinc measurements for 3 notebook locations
Text line:	.335	.374	.440
Witness line:	.210	.262	.188	.329	.439	.397
Intersection:	.393	.353	.285	.295	0.319

Calculation

Using RMD include the answers to the following questions:

Derive the formula for the confidence interval for a difference of means assuming independent samples and equal population variances. You may assume the formula for the pivotal statistic. (picture)
Put the final formula into Latex.
Make an R function (you may use t.test()) that will create 3 boxplots (one per category: "Text line", "Witness line" and "Intersection") on the one graphical interface and also print a list of all possible confidence intervals.
Do you think the assumption of equal population variances is justified?
Create Welsh intervals for the same set of differences in means. What do you conclude?

Quiz attempt 2 and 3

Good luck with your next attempts