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Confidence Intervals

Decoders often use the fact that the letter "e" appears in written work more than any other letter. Make a photocopy of an article in a newspaper or magazine {see article below}. Choose two different paragraphs from that article/page (must be a minimum of 25 words in each paragraph and the paragraphs must contain the letters e and c in them).

a. Determine the proportion of letters that are e's in your first paragraph.
b. Create a 95% confidence interval for the proportion of letters that are e's in your sample.
c. Determine the proportion of letters that are c's in your second paragraph.
d. Create a 95% confidence interval for the proportion of letters that are c's in your sample.
e. Based on the two confidence intervals that you created, could you conclude that the actual proportion of e's and c's in written work is different? Why or why not?

Article:

As for Weedsport, the No. 1 state-ranked Warriors have already set a school record for wins in one season, and they are the only unbeaten Class D team in the state. Now, coach Cal Mosher's Warriors will bid for the school's first-ever state team championship as they prepare to kick off against downstate champion Tuckahoe (8-2), a team that trounced Warrensburg 47-6.
Tuckahoe, No. 3 state-ranked last week, relies heavily on the backfield play of senior 5-10, 205-pound running back Axel Cortijo and 5-10, 170-pound senior quarterback Eliot Melendez. Against Warrenbsurg, Cortijo rushed for 253 yards on 22 carries and tallied three touchdowns, earning the MVP honor.

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Decoders often use the fact that the letter "e" appears in written work more than any other letter. Make a photocopy of an article in a newspaper or magazine {see article below}. Choose two different paragraphs from that article/page (must be a minimum of 25 words in each paragraph and the paragraphs must contain the letters e and c in them).

a. Determine the proportion of letters that are e's in your first paragraph.
b. Create a 95% confidence interval for the proportion of letters that are e's in your sample.
c. Determine the proportion of letters that are c's in your second paragraph.
d. Create a 95% confidence interval for the proportion of letters that are c's in your sample.
e. Based on the two confidence intervals that you created, could you conclude that the actual proportion of e's and c's in written work is different? Why or why not?

Article:

As for Weedsport, the No. 1 state-ranked Warriors have already set a school record for wins in one season, and they are the only unbeaten Class D team in the state. Now, coach Cal Mosher's Warriors will bid for the school's first-ever state team championship as they prepare to kick off against downstate champion Tuckahoe (8-2), a team that trounced Warrensburg 47-6.
Tuckahoe, No. 3 state-ranked last week, relies heavily on the backfield play of senior 5-10, 205-pound running back Axel Cortijo and 5-10, 170-pound senior quarterback Eliot Melendez. Against Warrenbsurg, Cortijo rushed for 253 yards on 22 carries and tallied three touchdowns, earning the MVP honor.

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