Pyramid Lake is on the Paiute Indian Reservation in Nevada. The lake is famous for cutthroat trout. Suppose a friend tells you that the average length of trout caught in Pyramid Lake is u = 19 inches. However, a survey reported that of a random sample of 51 fish caught, the mean length was x = 18.7 inches, with estimated standard deviation s = 3.1 inches. Do these data indicate that the average length of a trout caught in Pyramid Lake is less than H = 19 inches? Use a = 0.05. (a) What is the level of significance? State the null and alternate hypotheses. O Ho: u > 19 in; H1: µ = 19 in O Ho: H = 19 in; H1: u < 19 in O Họ: H = 19 in; H1: H + 19 in O Họ: H < 19 in; H1: H = 19 in O Họ: H = 19 in; H1: µ > 19 in (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. O The Student's t, since the sample size is large and o is unknown. O The standard normal, since the sample size is large and o is unknown. The Student's t, since the sample size is large and o is known. O The standard normal, since the sample size is large and o is known. What is the value of the sample test statistic? (Round your answer to three decimal places.) (c) Find the P-value. (Round your answer to four decimal places.)
Pyramid Lake is on the Paiute Indian Reservation in Nevada. The lake is famous for cutthroat trout. Suppose a friend tells you that the average length of trout caught in Pyramid Lake is u = 19 inches. However, a survey reported that of a random sample of 51 fish caught, the mean length was x = 18.7 inches, with estimated standard deviation s = 3.1 inches. Do these data indicate that the average length of a trout caught in Pyramid Lake is less than H = 19 inches? Use a = 0.05. (a) What is the level of significance? State the null and alternate hypotheses. O Ho: u > 19 in; H1: µ = 19 in O Ho: H = 19 in; H1: u < 19 in O Họ: H = 19 in; H1: H + 19 in O Họ: H < 19 in; H1: H = 19 in O Họ: H = 19 in; H1: µ > 19 in (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. O The Student's t, since the sample size is large and o is unknown. O The standard normal, since the sample size is large and o is unknown. The Student's t, since the sample size is large and o is known. O The standard normal, since the sample size is large and o is known. What is the value of the sample test statistic? (Round your answer to three 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
Related questions
Question
Transcribed Image Text:Pyramid Lake is on the Paiute Indian Reservation in Nevada. The lake is famous for cutthroat trout. Suppose a friend tells you that the average length of trout caught in Pyramid Lake is u = 19 inches.
However, a survey reported that of a random sample of 51 fish caught, the mean length was x = 18.7 inches, with estimated standard deviation s = 3.1 inches. Do these data indicate that the average
length of a trout caught in Pyramid Lake is less than u = 19 inches? Use a = 0.05.
(a) What is the level of significance?
State the null and alternate hypotheses.
О Но: и > 19in; Hi: и %3D 19 in
Ho: H = 19 in; H1: µ < 19 in
Ho: H = 19 in; H1: µ ± 19 in
Но: и < 19 in; Hi: и %3D 19 in
Но: и %3D 19 in; Hi: и > 19 in
(b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.
The Student's t, since the sample size is large and o is unknown.
The standard normal, since the sample size is large and o is unknown.
The Student's t, since the sample size is large and o is known.
The standard normal, since the sample size is large and o is known.
What is the value of the sample test statistic? (Round your answer to three decimal places.)
(c) Find the P-value. (Round your answer to four decimal places.)
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 2 images
Recommended textbooks for you
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
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
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
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
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
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
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman