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 = 18.6 inches, with estimated standard deviation s = 3.3 inches. Do these data indicate that the average length of a trout caught in Pyramid Lake is less than = 19 inches? Use a = 0.05. In USE SALT (a) What is the level of significance? State the null and alternate hypotheses. O Ho: H = 19 in; H,:H< 19 in O Ho: u > 19 in; H,: - 19 in O Hoi u < 19 in; H,: - 19 in O Hại H = 19 in; H,: > 19 in O Ho: H = 19 in; H,: H+ 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 known. O The standard normal, since the sample size is large and a is unknown. O The standard normal, since the sample size is large and o is known. O The Student's t, since the sample size is large and o is unknown. What is the value of the sample test statistic? (Round your answer to three decimal places.) (c) Estimate the P-value. O P-value > 0.010 O 0.0010 < P.value < 0.010 O 0.250 < P-value < 0.0010 O 0.125 < P-value < 0.250 O P-value < 0.125
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 = 18.6 inches, with estimated standard deviation s = 3.3 inches. Do these data indicate that the average length of a trout caught in Pyramid Lake is less than = 19 inches? Use a = 0.05. In USE SALT (a) What is the level of significance? State the null and alternate hypotheses. O Ho: H = 19 in; H,:H< 19 in O Ho: u > 19 in; H,: - 19 in O Hoi u < 19 in; H,: - 19 in O Hại H = 19 in; H,: > 19 in O Ho: H = 19 in; H,: H+ 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 known. O The standard normal, since the sample size is large and a is unknown. O The standard normal, since the sample size is large and o is known. O The Student's t, since the sample size is large and o is unknown. What is the value of the sample test statistic? (Round your answer to three decimal places.) (c) Estimate the P-value. O P-value > 0.010 O 0.0010 < P.value < 0.010 O 0.250 < P-value < 0.0010 O 0.125 < P-value < 0.250 O P-value < 0.125
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
A single question with sub-parts. Please answer them all step by step. Thank you
Transcribed Image Text:Sketch the sampling distribution and show the area corresponding to the P-value.
.2
2
4
-2
2
-2
4
4
-2
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 = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.
At the a = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.
O At the a = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.
O At the a = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.
(e) Interpret your conclusion in the context of the application.
O There is sufficient evidence at the 0.05 level to conclude that the average fish length is less than 19 inches.
O There is insufficient evidence at the 0.05 level to conclude that the average fish length is less than 19 inches.
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 = 18.6 inches, with estimated standard deviation s = 3.3 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.
n USE SALT
(a) What is the level of significance?
State the null and alternate hypotheses.
О Н: и 3D 19 in; H,: и < 19 in
Но: и> 19 in; Hi: и
= 19 in
Но: и < 19 in; H: и
= 19 in
О Н: и 3 19 in; H,: и > 19 in
О Но: и 3D 19 in; H,: 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 known.
O The standard normal, since the sample size is large and o is unknown.
The standard normal, since the sample size is large and o is known.
O The Student's t, since the sample size is large and o is unknown.
What is the value of the sample test statistic? (Round your answer to three decimal places.)
(c) Estimate the P-value.
O P-value > 0.010
O 0.0010 < P-value < 0.010
0.250 < P-value < 0.0010
O 0.125 < P-value < 0.250
P-value < 0.125
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 3 steps with 3 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.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