Allen’s hummingbird (*Selasphorus sasin*) has been studied by zoologist Bill Alther.† Suppose a small group of 20 Allen’s hummingbirds has been under study in Arizona. The average weight for these birds is x = 3.70 grams. Based on previous studies, we can assume that the weights of Allen’s hummingbirds have a normal distribution, with σ = 0.32 gram.

When finding an 86% confidence interval, what is the critical value for confidence level? (Give your answer to two decimal places.)

z_{c} =

(a)

Find an 86% 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

Find the minimum sample size necessary for an 86% confidence level with a maximal margin of error *E* = 0.15 for the mean weights of the hummingbirds. (Round your answer to a whole number.)

hummingbirds

Allen’s hummingbird (*Selasphorus sasin*) has been studied by zoologist Bill Alther.† Suppose a small group of 10 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.

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.)

hummingbirds

Allen’s hummingbird (*Selasphorus sasin*) has been studied by zoologist Bill Alther.† Suppose a small group of 12 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 ? = 0.36 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.)

*n* is large

lower limit | |

upper limit | |

margin of error |

(b) What conditions are necessary for your calculations? (Select all that apply.)

? is unknown

uniform distribution of weights

? is known

normal distribution of weights

(c) Interpret your results in the context of this problem. pick 1 from 1-4

1. The probability that this interval contains the true average weight of Allen’s hummingbirds is 0.20.

2. We are 20% confident that the true average weight of Allen’s hummingbirds falls within this interval.

3.We are 80% confident that the true average weight of Allen’s hummingbirds falls within this interval.

4.The probability that this interval contains the true average weight of Allen’s hummingbirds is 0.80.

(d) Find the sample size necessary for an 80% confidence level with a maximal margin of error *E* = 0.16 for the mean weights of the hummingbirds. (Round up to the nearest whole number.)

Allen’s hummingbird (*Selasphorus sasin*) has been studied by zoologist Bill Alther.† Suppose a small group of 17 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 ? = 0.34 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.)

? is knownuniform distribution of weights? is unknown*n* is largenormal distribution of weights

(c) Interpret your results in the context of this problem.

The probability that this interval contains the true average weight of Allen’s hummingbirds is 0.20. We are 80% confident that the true average weight of Allen’s hummingbirds falls within this interval. The probability that this interval contains the true average weight of Allen’s hummingbirds is 0.80.We are 20% confident that the true average weight of Allen’s hummingbirds falls within this interval.

(d) Find the sample size necessary for an 80% confidence level with a maximal margin of error *E* = 0.11 for the mean weights of the hummingbirds. (Round up to the nearest whole number.)

hummingbirds

Allen’s hummingbird (*Selasphorus sasin*) has been studied by zoologist Bill Alther.† Suppose a small group of 17 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 |

Allen’s hummingbird (*Selasphorus sasin*) has been studied by zoologist Bill Alther.† Suppose a small group of 13 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 = 0.20 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

Allen’s hummingbird (*Selasphorus sasin*) has been studied by zoologist Bill Alther.† Suppose a small group of 10 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 = 0.22 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.)

uniform distribution of weightsσ is knownσ is unknown*n* is largenormal distribution of weights

(c) Interpret your results in the context of this problem.

We are 20% confident that the true average weight of Allen’s hummingbirds falls within this interval. We are 80% confident that the true average weight of Allen’s hummingbirds falls within this interval. The probability that this interval contains the true average weight of Allen’s hummingbirds is 0.80.The probability that this interval contains the true average weight of Allen’s hummingbirds is 0.20.

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) 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.)

_________hummingbirds

**1)**

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.)

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.

Allen’s hummingbird (*Selasphorus sasin*) has been studied by zoologist Bill Alther.† Suppose a small group of 14 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 = 0.38 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.)

σ is knownσ is unknown*n* is largenormal distribution of weightsuniform distribution of weights

(c) Interpret your results in the context of this problem.

We are 80% confident that the true average weight of Allen’s hummingbirds falls within this interval.The probability that this interval contains the true average weight of Allen’s hummingbirds is 0.80. The probability that this interval contains the true average weight of Allen’s hummingbirds is 0.20.We are 20% confident that the true average weight of Allen’s hummingbirds falls within this interval.

(d) Find the sample size necessary for an 80% confidence level with a maximal margin of error *E* = 0.15 for the mean weights of the hummingbirds. (Round up to the nearest whole number.)

hummingbirds

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