logist 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 or= 0.88 gram. Suppose it is known that for the population of all Anna's hummingbirds, the mean weight is μ = 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 x = 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? OH μ< 4.65 g; H = 4.65 g; left-tailed OH = 4.65 g; Hμ> 4.65 g; right-tailed OH = 4.65 g; H₂ μ< 4.65 g; left-tailed H₁ μ = 4.65 g; H₁4.65 g; two-tailed (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. O The standard normal distribution, since we assume that x has a normal distribution with known o O The t distribution, since n is large with unknown or O The t distribution, since we assume that x has a normal distribution with known o O The standard normal distribution, since we assume that x has a normal distribution with unknown or Compute the value of the z test statistic. (Round your answer to two decimal places.) (c) Find the P-value. (Round your answer to four decimal places.)
logist 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 or= 0.88 gram. Suppose it is known that for the population of all Anna's hummingbirds, the mean weight is μ = 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 x = 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? OH μ< 4.65 g; H = 4.65 g; left-tailed OH = 4.65 g; Hμ> 4.65 g; right-tailed OH = 4.65 g; H₂ μ< 4.65 g; left-tailed H₁ μ = 4.65 g; H₁4.65 g; two-tailed (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. O The standard normal distribution, since we assume that x has a normal distribution with known o O The t distribution, since n is large with unknown or O The t distribution, since we assume that x has a normal distribution with known o O The standard normal distribution, since we assume that x has a normal distribution with unknown or Compute the value of the z test statistic. (Round your answer to two decimal places.) (c) Find 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
Section: Chapter Questions
Problem 1P
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Question
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= 0.88 gram. Suppose it is
known that for the population of all Anna's hummingbirds, the mean weight is = 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
x=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?
OH μ< 4.65 g; H
= 4.65 g; left-tailed
OH
= 4.65 g; H₂ μ> 4.65 g; right-tailed
OH
= 4.65 g; H₂ μ< 4.65 g; left-tailed
OH
= 4.65 g; Hμ 4.65 g; two-tailed
(b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.
O The standard normal distribution, since we assume that x has a normal distribution with known o
O The t distribution, since n is large with unknown o
O The t distribution, since we assume that x has a normal distribution with known o
O The standard normal distribution, since we assume that x has a normal distribution with unknown or.
Compute the value of the z test statistic. (Round your answer to two decimal places.)
(c) Find the P-value. (Round your answer to four decimal places.)
Expert Solution
Step 1: Define the data.
From the information, given that
The claim is to test whether the mean weight of the birds in this part of the Grand Canyon is less than 4.65 grams or not.
Step by step
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