/2 (d) Will the researcher reject the null hypothesis? O A. No, because the test statistic does not fall in the critical region. O B. No, because the test statistic falls in the critical region. O c. Yes, because the test statistic does not fall in the critical region. O D. Yes, because the test statistic falls in the critical region.
/2 (d) Will the researcher reject the null hypothesis? O A. No, because the test statistic does not fall in the critical region. O B. No, because the test statistic falls in the critical region. O c. Yes, because the test statistic does not fall in the critical region. O D. Yes, because the test statistic falls in the critical region.
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 4
Answer part D only!!
![To test \( H_0: \mu = 40 \) versus \( H_1: \mu < 40 \), a random sample of size \( n = 25 \) is obtained from a population that is known to be normally distributed. Complete parts (a) through (d) below.
**(a)** If \( \bar{x} = 37.4 \) and \( s = 13.6 \), compute the test statistic.
\[ t_0 = -0.956 \] (Round to three decimal places as needed.)
**(b)** If the researcher decides to test this hypothesis at the \( \alpha = 0.05 \) level of significance, determine the critical value(s). Although technology or a t-distribution table can be used to find the critical value, in this problem use the t-distribution table given.
\[ \text{Critical Value: } -1.711 \] (Round to three decimal places. Use a comma to separate answers as needed.)
**(c)** Draw a t-distribution that depicts the critical region. Choose the correct answer below.
- Option A shows a distribution with the critical region on the right tail.
- **Option B** shows a distribution with the critical region on the left tail, marked at \(-t_{\alpha}\).
- Option C shows a distribution with critical regions on both tails.
**(d)** Will the researcher reject the null hypothesis?
- \( \circ \) A. No, because the test statistic does not fall in the critical region.
- \( \circ \) **B. No, because the test statistic falls in the critical region.**
- \( \circ \) C. Yes, because the test statistic does not fall in the critical region.
- \( \circ \) D. Yes, because the test statistic falls in the critical region.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2222e4f0-f1eb-45aa-b497-401af5275439%2F66b52e08-9bb9-489b-a719-6cc96aacc83d%2Fhukhmko_processed.png&w=3840&q=75)
Transcribed Image Text:To test \( H_0: \mu = 40 \) versus \( H_1: \mu < 40 \), a random sample of size \( n = 25 \) is obtained from a population that is known to be normally distributed. Complete parts (a) through (d) below.
**(a)** If \( \bar{x} = 37.4 \) and \( s = 13.6 \), compute the test statistic.
\[ t_0 = -0.956 \] (Round to three decimal places as needed.)
**(b)** If the researcher decides to test this hypothesis at the \( \alpha = 0.05 \) level of significance, determine the critical value(s). Although technology or a t-distribution table can be used to find the critical value, in this problem use the t-distribution table given.
\[ \text{Critical Value: } -1.711 \] (Round to three decimal places. Use a comma to separate answers as needed.)
**(c)** Draw a t-distribution that depicts the critical region. Choose the correct answer below.
- Option A shows a distribution with the critical region on the right tail.
- **Option B** shows a distribution with the critical region on the left tail, marked at \(-t_{\alpha}\).
- Option C shows a distribution with critical regions on both tails.
**(d)** Will the researcher reject the null hypothesis?
- \( \circ \) A. No, because the test statistic does not fall in the critical region.
- \( \circ \) **B. No, because the test statistic falls in the critical region.**
- \( \circ \) C. Yes, because the test statistic does not fall in the critical region.
- \( \circ \) D. Yes, because the test statistic falls in the critical region.
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