(3-B is needed to answer it I am only asking for question 4.) 3) You go out and collect the following estimates of earthworms / acre: 54,276 57,378 51,108 66,190 66,232 59,018 57,159 These data yield the following: ̄y = 59,765.86, and s = 5,689.606 a) Construct a 90% CI for these data. b) Construct a 99% CI for these data. c) Darwin once estimated that an acre of soil had about 50,000 worms in it. Is his estimate consistent with the data above? (Historical note: His estimate was considered way too high in his day). 4) Consider the results of 3(b). Notice that all the data fit within the 99% confidence interval. Is this usually the case (in other words, will a 99% CI contain most of the observations)? Caution: a lot of people get this wrong! Here's a hint: suppose you had measured the worms in 6000 acres (instead of just 7). What happens to the confidence interval? If you're not sure, substitute 6,000 for 7 in your calculation for (b) to see what happens.
(3-B is needed to answer it I am only asking for question 4.)
3) You go out and collect the following estimates of earthworms / acre:
54,276 57,378 51,108 66,190 66,232 59,018 57,159
These data yield the following: ̄y = 59,765.86, and s = 5,689.606
a) Construct a 90% CI for these data.
b) Construct a 99% CI for these data.
c) Darwin once estimated that an acre of soil had about 50,000 worms in it. Is his estimate
consistent with the data above? (Historical note: His estimate was considered way too high in
his day).
4) Consider the results of 3(b). Notice that all the data fit within the 99% confidence interval. Is this
usually the case (in other words, will a 99% CI contain most of the observations)?
Caution: a lot of people get this wrong! Here's a hint: suppose you had measured the worms in
6000 acres (instead of just 7). What happens to the confidence interval? If you're not sure,
substitute 6,000 for 7 in your calculation for (b) to see what happens.
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