Bill Alther is a zoologist who studies Anna's hummingbird (Calypte anna). (Reference: Hummingbirds, K. Long, W. Alther.) 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 o = 0.64 gram. Suppose it is known that for the population of all Anna's hummingbirds, the mean weight is u = 4.30 grams. Do the data indicate that the mean weight of these birds in this part of the Grand Canyon is less than 4.30 grams? Use a = 0.10. %3D (a) What is the level of significance? (Enter a number.) State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test? O Ho: 4 < 4.3 g; H1: µ = 4.3 g; left-tailed O Ho: H = 4.3 g; H: µ > 4.3 g; right-tailed O Họ: u = 4.3 g; H: µ < 4.3 g; left-tailed O Họ: 4 = 4.3 g; H: µ # 4.3 g; two-tailed (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. O The standard normal, since we assume that x has a normal distribution with unknown a. O The Student's t, since we assume that x has a normal distribution with known o. O The Student's t, since n is large with unknown o. O The standard normal, since we assume that x has a normal distribution with known o. Compute the z value of the sample test statistic, (Enter a number. Round your answer to two decimal places.) (c) Find (or estimate) the P-value. (Enter a number. Round your answer to four decimal places.) Sketch the sampling distribution and show the area corresponding to the P-value. (Select the correct graph.) 3. -1 -2 -3 12:52 PM 1/8/2020

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.4: Distributions Of Data
Problem 19PFA
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Bill Alther is a zoologist who studies Anna's hummingbird (Calypte anna). (Reference: Hummingbirds, K. Long, W. Alther.) 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 o = 0.64 gram. Suppose it is known that for the population of all Anna's hummingbirds,
the mean weight is u = 4.30 grams. Do the data indicate that the mean weight of these birds in this part of the Grand Canyon is less than 4.30 grams? Use a = 0.10.
%3D
(a) What is the level of significance? (Enter a number.)
State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test?
O Ho: 4 < 4.3 g; H1: µ = 4.3 g; left-tailed
O Ho: H = 4.3 g; H: µ > 4.3 g; right-tailed
O Họ: u = 4.3 g; H: µ < 4.3 g; left-tailed
O Họ: 4 = 4.3 g; H: µ # 4.3 g; two-tailed
(b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.
O The standard normal, since we assume that x has a normal distribution with unknown a.
O The Student's t, since we assume that x has a normal distribution with known o.
O The Student's t, since n is large with unknown o.
O The standard normal, since we assume that x has a normal distribution with known o.
Compute the z value of the sample test statistic, (Enter a number. Round your answer to two decimal places.)
(c) Find (or estimate) the P-value. (Enter a number. Round your answer to four decimal places.)
Sketch the sampling distribution and show the area corresponding to the P-value. (Select the correct graph.)
3.
-1
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12:52 PM
1/8/2020
Transcribed Image Text:Bill Alther is a zoologist who studies Anna's hummingbird (Calypte anna). (Reference: Hummingbirds, K. Long, W. Alther.) 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 o = 0.64 gram. Suppose it is known that for the population of all Anna's hummingbirds, the mean weight is u = 4.30 grams. Do the data indicate that the mean weight of these birds in this part of the Grand Canyon is less than 4.30 grams? Use a = 0.10. %3D (a) What is the level of significance? (Enter a number.) State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test? O Ho: 4 < 4.3 g; H1: µ = 4.3 g; left-tailed O Ho: H = 4.3 g; H: µ > 4.3 g; right-tailed O Họ: u = 4.3 g; H: µ < 4.3 g; left-tailed O Họ: 4 = 4.3 g; H: µ # 4.3 g; two-tailed (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. O The standard normal, since we assume that x has a normal distribution with unknown a. O The Student's t, since we assume that x has a normal distribution with known o. O The Student's t, since n is large with unknown o. O The standard normal, since we assume that x has a normal distribution with known o. Compute the z value of the sample test statistic, (Enter a number. Round your answer to two decimal places.) (c) Find (or estimate) the P-value. (Enter a number. Round your answer to four decimal places.) Sketch the sampling distribution and show the area corresponding to the P-value. (Select the correct graph.) 3. -1 -2 -3 12:52 PM 1/8/2020
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