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 ? = 0.98 gram. Suppose it is known that for the population of all Anna's hummingbirds, the mean weight is ? = 4.80 grams. Do the data indicate that the mean weight of these birds in this part of the Grand Canyon is less than 4.80 grams? Use ? = 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: ? = 4.8 g; H1: ? ≠ 4.8 g; two-tailedH0: ? < 4.8 g; H1: ? = 4.8 g; left-tailed     H0: ? = 4.8 g; H1: ? > 4.8 g; right-tailedH0: ? = 4.8 g; H1: ? < 4.8 g; left-tailed (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. The standard normal, since we assume that x has a normal distribution with known ?.The standard normal, since we assume that x has a normal distribution with unknown ?.     The Student's t, since we assume that x has a normal distribution with known ?.The Student's t, since n is large with unknown ?. 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.) Sketch the sampling distribution and show the area corresponding to the P-value.

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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. 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 ? = 0.98 gram. Suppose it is known that for the population of all Anna's hummingbirds, the mean weight is ? = 4.80 grams. Do the data indicate that the mean weight of these birds in this part of the Grand Canyon is less than 4.80 grams? Use ? = 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: ? = 4.8 g; H1: ? ≠ 4.8 g; two-tailedH0: ? < 4.8 g; H1: ? = 4.8 g; left-tailed     H0: ? = 4.8 g; H1: ? > 4.8 g; right-tailedH0: ? = 4.8 g; H1: ? < 4.8 g; left-tailed

(b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.
The standard normal, since we assume that x has a normal distribution with known ?.The standard normal, since we assume that x has a normal distribution with unknown ?.     The Student's t, since we assume that x has a normal distribution with known ?.The Student's t, since n is large with unknown ?.

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.)


Sketch the sampling distribution and show the area corresponding to the P-value. 
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