Bill Alther is a zoologist who studies Anna's hummingbird ( Calypte anna ).† Suppose that in a remote part of the Grand Canyon, a random sample of six of these birds was caught, weighed, and released....

Bill Alther is a zoologist who studies Anna's hummingbird (Calypte anna).† Suppose that in a remote part of the Grand Canyon, a random sample of six of these birds was caught, weighed, and released. The weights (in grams) were as follows.

3.7

2.9

3.8

4.2

4.8

3.1

The sample mean is x = 3.75 grams. Letx be a random variable representing weights of hummingbirds in this part of the Grand Canyon. We assume thatx has a normal distribution and σ = 1.00 gram. Suppose it is known that for the population of all Anna's hummingbirds, the mean weight is μ = 4.75 grams. Do the data indicate that the mean weight of these birds in this part of the Grand Canyon is less than 4.75 grams? Use α = 0.01.

(a) What is the level of significance?

State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test?

H
₀: μ < 4.75="">H
₁: μ = 4.75 g; left-tailedH
₀: μ = 4.75 g;H
₁: μ < 4.75="" g;="">H
₀: μ = 4.75 g;H
₁: μ ≠ 4.75 g; two-tailedH
₀: μ = 4.75 g;H
₁: μ > 4.75 g; right-tailed

(b)Compute the
z value of the sample test statistic. (Round your answer to two decimal places.)

(c) Find (or estimate) the
P-value. (Round your answer to four decimal places.)

Jun 02, 2022

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Bill Alther is a zoologist who studies Anna's hummingbird ( Calypte anna ).† Suppose that in a remote part of the Grand Canyon, a random sample of six of these birds was caught, weighed, and released....

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