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. (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: H< 4.3 g; H,: u = 4.3 g; left-tailed Ho: u = 4.3 g; H,: u # 4.3 g; two-tailed O Ho: u = 4.3 g; H,: u < 4.3 g; left-tailed O Ho: H = 4.3 g; H,: u > 4.3 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 n is large with unknown o. O The standard normal, since we assume that x has a normal distribution with unknown o. O The standard normal, since we assume that x has a normal distribution with known 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. (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 t the P-value. (Select the correct graph.)
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. (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: H< 4.3 g; H,: u = 4.3 g; left-tailed Ho: u = 4.3 g; H,: u # 4.3 g; two-tailed O Ho: u = 4.3 g; H,: u < 4.3 g; left-tailed O Ho: H = 4.3 g; H,: u > 4.3 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 n is large with unknown o. O The standard normal, since we assume that x has a normal distribution with unknown o. O The standard normal, since we assume that x has a normal distribution with known 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. (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 t the P-value. (Select the correct graph.)
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Topic Video
Question
(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?
(b)
What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.
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.)
d)
Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level α?
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.
(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: H< 4.3 g; H,: u = 4.3 g; left-tailed
Ho: u = 4.3 g; H,: u # 4.3 g; two-tailed
O Ho: u = 4.3 g; H,: u < 4.3 g; left-tailed
O Ho: H = 4.3 g; H,: u > 4.3 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 n is large with unknown o.
O The standard normal, since we assume that x has a normal distribution with unknown o.
O The standard normal, since we assume that x has a normal distribution with known 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. (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 t the P-value. (Select the correct graph.)
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