Homework Help is Here – Start Your Trial Now!
Math
Statistics
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) we as follows. 3.7 2.9 3.8 42 48 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 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 a=0.10. (a) What is the level of significance? 0.10 State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test? OH <4.65 g; Hu=4.65 g; left-tailed OH=4.65 g; H₁>4.65 g; right-tailed ⒸH₂=4.65 g; Hu<4.65 g; left-tailed OH = 4.65 g; H₂ 4.65 g. two-tailed (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. The standard normal distribution, since we assume that x has a normal distribution with known a O The t distribution, since n is large with unknown o O The r distribution, since we assume that x has a normal distribution with known or O The standard normal distribution, since we assume that x has a normal distribution with unknown o Compute the value of the z test statistic. (Round your answer to two decimal places.) -2.51 (c) Find the P-value. (Round your answer to four decimal places.) 0.0060 Sketch the sampling distribution and show the area corresponding to the P-value.

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) we as follows. 3.7 2.9 3.8 42 48 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 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 a=0.10. (a) What is the level of significance? 0.10 State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test? OH <4.65 g; Hu=4.65 g; left-tailed OH=4.65 g; H₁>4.65 g; right-tailed ⒸH₂=4.65 g; Hu<4.65 g; left-tailed OH = 4.65 g; H₂ 4.65 g. two-tailed (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. The standard normal distribution, since we assume that x has a normal distribution with known a O The t distribution, since n is large with unknown o O The r distribution, since we assume that x has a normal distribution with known or O The standard normal distribution, since we assume that x has a normal distribution with unknown o Compute the value of the z test statistic. (Round your answer to two decimal places.) -2.51 (c) Find the P-value. (Round your answer to four decimal places.) 0.0060 Sketch the sampling distribution and show the area corresponding to the P-value.

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
Problem 1P
See similar textbooks
icon
Related questions
Question
Need help on the graph d and e
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 42 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 α = 0.10. (a) What is the level of significance? 0.10 State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test? OH <4.65 g; H = 4.65 g; left-tailed LL = 4.65 g; H>4.65 g; right-tailed OH ⒸH=4.65 g; Hu<4.65 g; left-tailed OH = 4.65 g; H₂4.65 g, two-tailed (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. The standard normal distribution, since we assume that x has a normal distribution with known a 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 o. Compute the value of the z test statistic. (Round your answer to two decimal places.) -2.51 (c) Find the P-value. (Round your answer to four decimal places.) 0.0060 Sketch the sampling distribution and show the area corresponding to the P-value.
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 42 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 α = 0.10. (a) What is the level of significance? 0.10 State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test? OH <4.65 g; H = 4.65 g; left-tailed LL = 4.65 g; H>4.65 g; right-tailed OH ⒸH=4.65 g; Hu<4.65 g; left-tailed OH = 4.65 g; H₂4.65 g, two-tailed (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. The standard normal distribution, since we assume that x has a normal distribution with known a 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 o. Compute the value of the z test statistic. (Round your answer to two decimal places.) -2.51 (c) Find the P-value. (Round your answer to four decimal places.) 0.0060 Sketch the sampling distribution and show the area corresponding to the P-value.
(c) Find the P-value. (Round your answer to four decimal places.) 0.0060 Sketch the sampling distribution and show the area corresponding to the P-value. -3 0-3 -2 -2 -1 0 -1 0 1 1 2 2 A -2 3 3 0-3 0-3 -2 -1 -1 0 0 1 1 2 2 (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 (? At the = 0.10 levell, we reject the null hypothesis and conclude the data are statistically significant. At the X = 0.10 level, we reject the null hypothesis and conclude the data are not statistically significant. At the X = 0.10 level, we fail to reject the null hypothesis and conclude the data are statistically significant. At the = 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. There is sufficient evidence at the 0.10 level to conclude that humming birds in the Grand Canyon weigh less than 4.65 grams. There is insufficient evidence at the 0.10 level to conclude that humming birds in the Grand Canyon weigh less than 4.65 grams. 3 3
Transcribed Image Text:(c) Find the P-value. (Round your answer to four decimal places.) 0.0060 Sketch the sampling distribution and show the area corresponding to the P-value. -3 0-3 -2 -2 -1 0 -1 0 1 1 2 2 A -2 3 3 0-3 0-3 -2 -1 -1 0 0 1 1 2 2 (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 (? At the = 0.10 levell, we reject the null hypothesis and conclude the data are statistically significant. At the X = 0.10 level, we reject the null hypothesis and conclude the data are not statistically significant. At the X = 0.10 level, we fail to reject the null hypothesis and conclude the data are statistically significant. At the = 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. There is sufficient evidence at the 0.10 level to conclude that humming birds in the Grand Canyon weigh less than 4.65 grams. There is insufficient evidence at the 0.10 level to conclude that humming birds in the Grand Canyon weigh less than 4.65 grams. 3 3
Expert Solution
Step 1: Deternine the given variables.

The question is about hypothesis testing.

Given :

Population standard deviation of the weight ( sigma ) = 0.88 grams

Randomly selected no. of birds ( n ) = 6

Sample mean weight ( x with bar on top ) = 3.75 grams

Population mean weight ( mu ) = 4.65 grams

Statistics homework question answer, step 1, image 1


To find :

Test whether the mean weight of the birds is less than 4.65 gram?

steps

Step by step

Solved in 6 steps with 19 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman
SEE MORE TEXTBOOKS