The data file includes the text of three books of the Bible (Joshua, Jonah and Philippians) using the ESV translation. While these are all great books, our only interest for this project is how often each letter is used. 3) Identify those letters whose Cls do not overlap with any the CIs of any of the other letters. (For example the CI [0.042, 0.052] overlaps with [0.050, 0.060] because the upper bound of the first CI is greater than the lower bound of the second CI.) List the letters with the non-overlapping Cis and specify how many such letters there are Question 3 answers: Letters Lower bound Upper bound L 0.037072109 0.042042 D 0.043728076 0.049092 E 0.11621383 0.12451 4) The previous analysis could be useful if our goal was to decipher an encrypted message, where each letter is scrambled (for example, each “a” might become a “g”, while each “b” might become an “o” and so forth). a) Assume that the letter “z” in encrypted message has a relative frequency of 0.06 (it accounts for 6% of the total number of letters). Which letter’s Confidence Intervals from question 3 contain 0.06 and thus are the most likely candidates to be the letter which was encrypted as “z”? b) Further assume that “y” in the encrypted message has a relative frequency of 0.04 (4%). Which letter’s question CIs contain 0.04? c) If “x” in the encrypted message has a relative frequency of 0.02 (2%), which letter’s question 3 CIs contain 0.02?
The data file includes the text of three books of the Bible (Joshua, Jonah and Philippians) using the ESV translation. While these are all great books, our only interest for this project is how often each letter is used.
3) Identify those letters whose Cls do not overlap with any the CIs of any of the other letters. (For example the CI [0.042, 0.052] overlaps with [0.050, 0.060] because the upper bound of the first CI is greater than the lower bound of the second CI.) List the letters with the non-overlapping Cis and specify how many such letters there are
Question 3 answers:
| Letters | Lower bound | Upper bound |
| L | 0.037072109 | 0.042042 |
| D | 0.043728076 | 0.049092 |
| E | 0.11621383 | 0.12451 |
4) The previous analysis could be useful if our goal was to decipher an encrypted message, where each letter is scrambled (for example, each “a” might become a “g”, while each “b” might become an “o” and so forth).
a) Assume that the letter “z” in encrypted message has a relative frequency of 0.06 (it accounts for 6% of the total number of letters). Which letter’s Confidence Intervals from question 3 contain 0.06 and thus are the most likely candidates to be the letter which was encrypted as “z”?
b) Further assume that “y” in the encrypted message has a relative frequency of 0.04 (4%). Which letter’s question CIs contain 0.04?
c) If “x” in the encrypted message has a relative frequency of 0.02 (2%), which letter’s question 3 CIs contain 0.02?
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what is the exact equation used for the lower and upper bound in excel?
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