TATE: Lyme disease is spread in the northeastern United States by infected ticks. The ticks are infected mainly by feeding on mice, so more mice result in more infected ticks. The mouse population rises and falls with the abundance of acorns, their favored food. Experimenters studied two similar forest areas in a year when the acorn crop failed. They added hundreds of thousands of acorns to one area to imitate an abundant acorn crop, while leaving the other area untouched. The next spring, 54 of the 72 mice trapped in the first area were in breeding condition, versus 10 of the 17 mice trapped in the second area. Estimate the difference between the proportions of mice ready to breed in good acorn years and bad acorn years. (Use 90% confidence. Be sure to justify your choice of confidence interval.) PLAN: Let ?1 and ?2 be (respectively) the proportions of mice ready to breed in good acorn years and bad acorn years. Give a 90% confidence interval for ?1−?2. Can the large‑sample method be used to find a 90% confidence interval for ?1−?2? Yes, because there is a large enough sample to use the large‑sample method. Yes, because all counts are at least 5. No, because all counts need to be at least 10 to use the large‑sample method. No, because the sample is not large enough to use the large‑sample method. SOLVE: Use the plus four method to find p~1 , ?̃ 2 , and the upper and lower bound of the 90% confidence interval. Give your answers to four decimal places. ?̃ 1= ?̃ 2= lower bound: upper bound: CONCLUDE: Which statement is best supported by the calculated values? There is 90% confidence that the proportion of mice ready to breed in good acorn years is between 0.04 lower than and 0.37 higher than the proportion in bad acorn years. No definitive conclusions using these values can be made. A percentage of 90% of the mice ready to breed in good acorn years is between 0.04 lower than and 0.37 higher than the proportion in bad acorn years. There is 90% confidence that the proportion of mice ready to breed in good acorn years is between 0.4 and 0.63 higher than the proportion in bad acorn years.
STATE: Lyme disease is spread in the northeastern United States by infected ticks. The ticks are infected mainly by feeding on mice, so more mice result in more infected ticks. The mouse population rises and falls with the abundance of acorns, their favored food. Experimenters studied two similar forest areas in a year when the acorn crop failed. They added hundreds of thousands of acorns to one area to imitate an abundant acorn crop, while leaving the other area untouched. The next spring, 54 of the 72 mice trapped in the first area were in breeding condition, versus 10 of the 17 mice trapped in the second area. Estimate the difference between the proportions of mice ready to breed in good acorn years and bad acorn years. (Use 90% confidence. Be sure to justify your choice of confidence interval.)
PLAN: Let ?1 and ?2 be (respectively) the proportions of mice ready to breed in good acorn years and bad acorn years. Give a 90% confidence interval for ?1−?2.
Can the large‑sample method be used to find a 90% confidence interval for ?1−?2?
Yes, because there is a large enough sample to use the large‑sample method.
Yes, because all counts are at least 5.
No, because all counts need to be at least 10 to use the large‑sample method.
No, because the sample is not large enough to use the large‑sample method.
SOLVE: Use the plus four method to find p~1 , ?̃ 2 , and the upper and lower bound of the 90% confidence interval. Give your answers to four decimal places.
CONCLUDE: Which statement is best supported by the calculated values?
There is 90% confidence that the proportion of mice ready to breed in good acorn years is between 0.04 lower than and 0.37 higher than the proportion in bad acorn years.
No definitive conclusions using these values can be made.
A percentage of 90% of the mice ready to breed in good acorn years is between 0.04 lower than and 0.37 higher than the proportion in bad acorn years.
There is 90% confidence that the proportion of mice ready to breed in good acorn years is between 0.4 and 0.63 higher than the proportion in bad acorn years.
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