(d) Approximate the P-value. Choose the correct answer below. A. 0.005 < P-value <0.01 B. 0.01
(d) Approximate the P-value. Choose the correct answer below. A. 0.005 < P-value <0.01 B. 0.01
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
Question 3
Answer Part D and Interpretation Only!!

Transcribed Image Text:The image displays a t-Distribution table, which provides critical t-values for various degrees of freedom (df) and tail areas. This table is used in statistics to determine the critical value of the t-distribution at a given significance level, particularly in hypothesis testing.
### Table Details:
- **df (Degrees of Freedom):** The first and last columns represent the degrees of freedom, ranging from 1 to 1000.
- **Columns for Areas in the Right Tail:** The top row lists probabilities or tail areas: 0.25, 0.20, 0.15, 0.10, 0.05, 0.025, 0.02, 0.01, 0.005, 0.0025, 0.001, 0.0005.
- **Values in the Table:** Each cell within the table corresponds to a critical t-value, which is used to determine the boundary at which the t-distribution's cumulative probability equals the specified areas in the right tail for the corresponding degrees of freedom.
For example, for a degree of freedom (df) of 10 and an area of 0.05 in the right tail, the critical t-value is 1.812 (from the 6th degree of freedom row, under the 0.05 column).
This table is essential for performing t-tests, especially when determining confidence intervals and hypothesis testing for small sample sizes in statistical analyses.
![To test \( H_0: \mu = 107 \) versus \( H_1: \mu \neq 107 \), a simple random sample of size \( n = 35 \) is obtained. Complete parts a through e below.
- **[Instruction to view t-Distribution Area in Right Tail]**
### (a)
- **Options:**
- C. Yes, because \( n \geq 30 \).
- D. No, because the test is two-tailed.
### (b) If \( \bar{x} = 103.8 \) and \( s = 5.9 \), compute the test statistic.
The test statistic is \( t_0 = -3.21 \). (Round to two decimal places as needed.)
### (c) Draw a t-distribution with the area that represents the P-value shaded. Choose the correct graph below.
- **Middle Graph**: A t-distribution with shading in both tails indicating a two-tailed test.
### (d) Approximate the P-value. Choose the correct answer below.
- **Options:**
- A. \( 0.005 < P\text{-value} < 0.01 \)
- B. \( 0.01 < P\text{-value} < 0.02 \)
- C. \( 0.002 < P\text{-value} < 0.005 \)
- D. \( 0.001 < P\text{-value} < 0.002 \)
### Interpret the P-value. Choose the correct answer below.
- **Options:**
- A. If 1000 random samples of size \( n = 35 \) are obtained, about 3 samples are expected to result in a mean as extreme or more extreme than the one observed if \( \mu = 103.8 \).
- B. If 1000 random samples of size \( n = 35 \) are obtained, about 3 samples are expected to result in a mean as extreme or more extreme than the one observed if \( \mu = 107 \).
- C. If 100 random samples of size \( n = 35 \) are obtained, about 3 samples are expected to result in a mean as extreme or more extreme than the one observed if \( \mu = 107 \).
- D. If 100](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2222e4f0-f1eb-45aa-b497-401af5275439%2F277ee24a-3b70-4807-b80f-c9061b42f536%2F3mxc30d_processed.png&w=3840&q=75)
Transcribed Image Text:To test \( H_0: \mu = 107 \) versus \( H_1: \mu \neq 107 \), a simple random sample of size \( n = 35 \) is obtained. Complete parts a through e below.
- **[Instruction to view t-Distribution Area in Right Tail]**
### (a)
- **Options:**
- C. Yes, because \( n \geq 30 \).
- D. No, because the test is two-tailed.
### (b) If \( \bar{x} = 103.8 \) and \( s = 5.9 \), compute the test statistic.
The test statistic is \( t_0 = -3.21 \). (Round to two decimal places as needed.)
### (c) Draw a t-distribution with the area that represents the P-value shaded. Choose the correct graph below.
- **Middle Graph**: A t-distribution with shading in both tails indicating a two-tailed test.
### (d) Approximate the P-value. Choose the correct answer below.
- **Options:**
- A. \( 0.005 < P\text{-value} < 0.01 \)
- B. \( 0.01 < P\text{-value} < 0.02 \)
- C. \( 0.002 < P\text{-value} < 0.005 \)
- D. \( 0.001 < P\text{-value} < 0.002 \)
### Interpret the P-value. Choose the correct answer below.
- **Options:**
- A. If 1000 random samples of size \( n = 35 \) are obtained, about 3 samples are expected to result in a mean as extreme or more extreme than the one observed if \( \mu = 103.8 \).
- B. If 1000 random samples of size \( n = 35 \) are obtained, about 3 samples are expected to result in a mean as extreme or more extreme than the one observed if \( \mu = 107 \).
- C. If 100 random samples of size \( n = 35 \) are obtained, about 3 samples are expected to result in a mean as extreme or more extreme than the one observed if \( \mu = 107 \).
- D. If 100
Expert Solution

This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps

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