Allen's hummingbird (Selasphorus sasin) has been studied by zoologist Bill Alther.† Suppose a small group of 11 Allen's hummingbirds has been under study in Arizona. The average weight for these birds is x = 3.15 grams. Based on previous studies, we can assume that the weights of Allen's hummingbirds have a normal distribution, with σ = 0.28 gram. (a) Find an 80% confidence interval for the average weights of Allen's hummingbirds in the study region. What is the margin of error? (Round your answers to two decimal places.) lower limit- upper limit- margin of error-   (b) What conditions are necessary for your calculations? (Select all that apply.)   (c) Interpret your results in the context of this problem.   (d) Find the sample size necessary for an 80% confidence level with a maximal margin of error E = 0.06 for the mean weights of the hummingbirds. (Round up to the nearest whole number.)   2) The method of tree ring dating gave the following years A.D. for an archaeological excavation site. Assume that the population of x values has an approximately normal distribution. 1236 1236 1306 1187 1268 1316 1275 1317 1275 (a) Use a calculator with mean and standard deviation keys to find the sample mean year x and sample standard deviation s. (Round your answers to the nearest whole number.) x =__________  A.D. s =__________  yr (b) Find a 90% confidence interval for the mean of all tree ring dates from this archaeological site. (Round your answers to the nearest whole number.) lower limit________ A.D. upper limit________ A.D.

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Allen's hummingbird (Selasphorus sasin) has been studied by zoologist Bill Alther.† Suppose a small group of 11 Allen's hummingbirds has been under study in Arizona. The average weight for these birds is x = 3.15 grams. Based on previous studies, we can assume that the weights of Allen's hummingbirds have a normal distribution, with σ = 0.28 gram.

(a) Find an 80% confidence interval for the average weights of Allen's hummingbirds in the study region. What is the margin of error? (Round your answers to two decimal places.)
lower limit-
upper limit-
margin of error-
 
(b) What conditions are necessary for your calculations? (Select all that apply.)
 
(c) Interpret your results in the context of this problem.
 
(d) Find the sample size necessary for an 80% confidence level with a maximal margin of error E = 0.06 for the mean weights of the hummingbirds. (Round up to the nearest whole number.)
 
2)
The method of tree ring dating gave the following years A.D. for an archaeological excavation site. Assume that the population of x values has an approximately normal distribution.
1236 1236 1306 1187 1268 1316 1275 1317 1275

(a) Use a calculator with mean and standard deviation keys to find the sample mean year x and sample standard deviation s. (Round your answers to the nearest whole number.)

x =__________  A.D.
s =__________  yr

(b) Find a 90% confidence interval for the mean of all tree ring dates from this archaeological site. (Round your answers to the nearest whole number.)

lower limit________ A.D.

upper limit________ A.D.

 

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