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StatisticsQ&A LibraryBill 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. Let x be a random variable representing weights of hummingbirds in this part of the Grand Canyon. We assume that x 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? H0: μ < 4.75 g; H1: μ = 4.75 g; left-tailedH0: μ = 4.75 g; H1: μ < 4.75 g; left-tailed H0: μ = 4.75 g; H1: μ ≠ 4.75 g; two-tailedH0: μ = 4.75 g; H1: 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.)Question

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. Let *x* be a random variable representing weights of hummingbirds in this part of the Grand Canyon. We assume that *x* 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 g; *H*_{1}: μ = 4.75 g; left-tailed*H*_{0}: μ = 4.75 g; *H*_{1}: μ < 4.75 g; left-tailed *H*_{0}: μ = 4.75 g; *H*_{1}: μ ≠ 4.75 g; two-tailed*H*_{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.)

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

(b)Compute the

(c) Find (or estimate) the

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