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 o = 0.90 gram. Suppose it is known that for the population of all Anna's hummingbirds, the mean weight is u = 4.65 grams. Do the data indicate that the mean weight of these birds in this part of the Grand Canyon is less than 4.65 grams? Use a = 0.10. (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? O H,i u = 4.65 g; H: u < 4.65 g; left-tailed O H,i u< 4.65 g; H,: u = 4.65 g; left-tailed O H,i u = 4.65 g; H,1 u 4.65 g: two-tailed O H,i u = 4.65 g:; H: u > 4.65 g; right-tailed (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. O The Student's t, since we assume that x has a normal distribution with known a. O The standard normal, since we assume that x has a normal distribution with known o. O The standard normal, since we assume that x has a normal distribution with unknown o. O The Student's t, since n is large with unknown a. 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. o-3 -1 1 o-3 -2
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 o = 0.90 gram. Suppose it is known that for the population of all Anna's hummingbirds, the mean weight is u = 4.65 grams. Do the data indicate that the mean weight of these birds in this part of the Grand Canyon is less than 4.65 grams? Use a = 0.10. (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? O H,i u = 4.65 g; H: u < 4.65 g; left-tailed O H,i u< 4.65 g; H,: u = 4.65 g; left-tailed O H,i u = 4.65 g; H,1 u 4.65 g: two-tailed O H,i u = 4.65 g:; H: u > 4.65 g; right-tailed (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. O The Student's t, since we assume that x has a normal distribution with known a. O The standard normal, since we assume that x has a normal distribution with known o. O The standard normal, since we assume that x has a normal distribution with unknown o. O The Student's t, since n is large with unknown a. 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. o-3 -1 1 o-3 -2
MATLAB: An Introduction with Applications
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ISBN:9781119256830
Author:Amos Gilat
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Chapter1: Starting With Matlab
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Transcribed Image Text: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 o = 0.90 gram. Suppose it is known that for the population of all Anna's hummingbirds, the mean
weight is u = 4.65 grams. Do the data indicate that the mean weight of these birds in this part of the Grand Canyon is less than 4.65 grams? Use a = 0.10.
(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?
O H,i u = 4.65 g; H: u < 4.65 g; left-tailed
O H,i u< 4.65 g; H,: u = 4.65 g; left-tailed
O H,i u = 4.65 g; H,1 u 4.65 g: two-tailed
O H,i u = 4.65 g:; H: u > 4.65 g; right-tailed
(b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.
O The Student's t, since we assume that x has a normal distribution with known a.
O The standard normal, since we assume that x has a normal distribution with known o.
O The standard normal, since we assume that x has a normal distribution with unknown o.
O The Student's t, since n is large with unknown a.
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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