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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 o=0.80 gram. Suppose it is known that for the population of all Anna's hummingbirds, the mean weight is μ = 4.50 grams. Do the data indicate that the mean weight of these birds in this part of t Grand Canyon is less than 4.50 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: = 4.5 g; H₁: > 4.5 g; right-tailed OH = 4.5 g; H₁: < 4.5 g; left-tailed O Ho: <4.5 g; H₁: = 4.5 g; left-tailed OH = 4.5 g; H₁: 4.5 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 o. O The Student's t, since n is large with unknown 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. 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. 4

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=0.80 gram. Suppose it is known that for the population of all Anna's hummingbirds, the mean weight is μ = 4.50 grams. Do the data indicate that the mean weight of these birds in this part of t Grand Canyon is less than 4.50 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: = 4.5 g; H₁: > 4.5 g; right-tailed OH = 4.5 g; H₁: < 4.5 g; left-tailed O Ho: <4.5 g; H₁: = 4.5 g; left-tailed OH = 4.5 g; H₁: 4.5 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 o. O The Student's t, since n is large with unknown 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. 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. 4

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
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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 = 0.80 gram. Suppose it is known that for the population of all Anna's hummingbirds, the mean weight is μ = 4.50 grams. Do the data indicate that the mean weight of these birds in this part of the Grand Canyon is less than 4.50 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: μ = 4.5 g; H₁: > 4.5 g; right-tailed O Ho: μ = 4.5 g; H₁: μ< 4.5 g; left-tailed O Ho: <4.5 g; H₁: μ = 4.5 g; left-tailed O Ho: μ = 4.5 g; H₁: μ + 4.5 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 σ. O The Student's t, since n is large with unknown o. O The Student's t, 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 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.) Sketch the sampling distribution and show the area corresponding to the P-value. 27
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 = 0.80 gram. Suppose it is known that for the population of all Anna's hummingbirds, the mean weight is μ = 4.50 grams. Do the data indicate that the mean weight of these birds in this part of the Grand Canyon is less than 4.50 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: μ = 4.5 g; H₁: > 4.5 g; right-tailed O Ho: μ = 4.5 g; H₁: μ< 4.5 g; left-tailed O Ho: <4.5 g; H₁: μ = 4.5 g; left-tailed O Ho: μ = 4.5 g; H₁: μ + 4.5 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 σ. O The Student's t, since n is large with unknown o. O The Student's t, 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 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.) Sketch the sampling distribution and show the area corresponding to the P-value. 27
0-3 0-3 -2 -1 - 2 -1 0 0 1 1 2 2 3 3 0-3 0-3 -2 -2 -1 -1 0 0 1 1 2 2 3 3 4 (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 a? O At the a = 0.10 level, we reject the null hypothesis and conclude the data are statistically significant. O At the a = 0.10 level, we reject the null hypothesis and conclude the data are not statistically significant. O At the a = 0.10 level, we fail to reject the null hypothesis and conclude the data are statistically significant. O At the a = 0.10 level, we fail to reject the null hypothesis and conclude the data are not statistically significant. (e) State your conclusion in the context of the application. O There is sufficient evidence at the 0.10 level to conclude that humming birds in the Grand Canyon weigh less than 4.50 grams. O There is insufficient evidence at the 0.10 level to conclude that humming birds in the Grand Canyon weigh less than 4.50 grams.
Transcribed Image Text:0-3 0-3 -2 -1 - 2 -1 0 0 1 1 2 2 3 3 0-3 0-3 -2 -2 -1 -1 0 0 1 1 2 2 3 3 4 (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 a? O At the a = 0.10 level, we reject the null hypothesis and conclude the data are statistically significant. O At the a = 0.10 level, we reject the null hypothesis and conclude the data are not statistically significant. O At the a = 0.10 level, we fail to reject the null hypothesis and conclude the data are statistically significant. O At the a = 0.10 level, we fail to reject the null hypothesis and conclude the data are not statistically significant. (e) State your conclusion in the context of the application. O There is sufficient evidence at the 0.10 level to conclude that humming birds in the Grand Canyon weigh less than 4.50 grams. O There is insufficient evidence at the 0.10 level to conclude that humming birds in the Grand Canyon weigh less than 4.50 grams.
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