Bill Alther is a zoologist who studies Anna's hummingbird (Calypte anna).t 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 = 1.00 gram. Suppose it is known that for the population of all Anna's hummingbirds, the mean welght 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-talled, or two-tailed test? O Ho: H = 4.65 g; H1: H < 4.65 g; left-tailed O Ho: 4 = 4.65 g; H: H > 4.65 g; right-tailed O Ho: H- 4.65 g; H: H * 4.65 g; two-tailed O Ho: H < 4.65 g; H1: H = 4.65 g; left-tailled (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. O The Student's t, since n is large with unknown a. O The standard normal, 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 unknown a. O The Student's t, since we assume that x has a normal distribution with known 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.)
Bill Alther is a zoologist who studies Anna's hummingbird (Calypte anna).t 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 = 1.00 gram. Suppose it is known that for the population of all Anna's hummingbirds, the mean welght 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-talled, or two-tailed test? O Ho: H = 4.65 g; H1: H < 4.65 g; left-tailed O Ho: 4 = 4.65 g; H: H > 4.65 g; right-tailed O Ho: H- 4.65 g; H: H * 4.65 g; two-tailed O Ho: H < 4.65 g; H1: H = 4.65 g; left-tailled (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. O The Student's t, since n is large with unknown a. O The standard normal, 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 unknown a. O The Student's t, since we assume that x has a normal distribution with known 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.)
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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Transcribed Image Text:Bill Alther is a zoologist who studies Anna's hummingbird (Calypte anna).t 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 = 1.00 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 Ho: H = 4.65 g; H1: H < 4.65 g; left-tailed
O Ho: H = 4.65 g; H1: µ > 4.65 g; right-tailed
O Ho: H = 4.65 g; H1: H # 4.65 g; two-tailed
O Ho: H < 4.65 g; H1: H = 4.65 g; left-tailed
(b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.
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.
The standard normal, since we assume that x has a normal distribution with unknown o.
O The Student's t, since we assume that x has a normal distribution with known o.
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.)
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