You wish to test the following claim (Ha) at a significance level of a = 0.01. Ho : μ = 82.5 H₂:μ> 82.5 You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n = 79 with a mean of M = 84.5 and a standard deviation of SD = 15.9. What is the critical value for this test? (Report answer accurate to three decimal places.) critical value = What is the test statistic for this sample? (Report answer accurate to three decimal places.) test statistic = The test statistic is... O in the critical region O not in the critical region
You wish to test the following claim (Ha) at a significance level of a = 0.01. Ho : μ = 82.5 H₂:μ> 82.5 You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n = 79 with a mean of M = 84.5 and a standard deviation of SD = 15.9. What is the critical value for this test? (Report answer accurate to three decimal places.) critical value = What is the test statistic for this sample? (Report answer accurate to three decimal places.) test statistic = The test statistic is... O in the critical region O not 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
![**Hypothesis Testing Example**
In this example, we aim to test the following claim (\(H_a\)) at a significance level of \(\alpha = 0.01\):
- Null Hypothesis (\(H_0\)): \(\mu = 82.5\)
- Alternative Hypothesis (\(H_a\)): \(\mu > 82.5\)
**Problem Statement:**
You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size \(n = 79\) with a mean of \(M = 84.5\) and a standard deviation of \(SD = 15.9\).
**Tasks:**
1. Determine the critical value for the test.
2. Calculate the test statistic for the sample.
3. Determine if the test statistic falls within the critical region.
**Critical Value Calculation:**
What is the critical value for this test? (Report the answer accurate to three decimal places.)
\[ \text{Critical value} = \]
**Test Statistic Calculation:**
What is the test statistic for this sample? (Report the answer accurate to three decimal places.)
\[ \text{Test statistic} = \]
**Conclusion:**
The test statistic is...
- ( ) in the critical region
- ( ) not in the critical region
By completing these steps, you can determine whether the test statistic falls within the critical region and thus make a decision about the null hypothesis \(H_0\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3268b88a-f4fb-4fae-897e-35b47f1612ff%2F3908ce4a-6b23-4305-9f71-20d42d288336%2Fw31emv9_processed.png&w=3840&q=75)
Transcribed Image Text:**Hypothesis Testing Example**
In this example, we aim to test the following claim (\(H_a\)) at a significance level of \(\alpha = 0.01\):
- Null Hypothesis (\(H_0\)): \(\mu = 82.5\)
- Alternative Hypothesis (\(H_a\)): \(\mu > 82.5\)
**Problem Statement:**
You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size \(n = 79\) with a mean of \(M = 84.5\) and a standard deviation of \(SD = 15.9\).
**Tasks:**
1. Determine the critical value for the test.
2. Calculate the test statistic for the sample.
3. Determine if the test statistic falls within the critical region.
**Critical Value Calculation:**
What is the critical value for this test? (Report the answer accurate to three decimal places.)
\[ \text{Critical value} = \]
**Test Statistic Calculation:**
What is the test statistic for this sample? (Report the answer accurate to three decimal places.)
\[ \text{Test statistic} = \]
**Conclusion:**
The test statistic is...
- ( ) in the critical region
- ( ) not in the critical region
By completing these steps, you can determine whether the test statistic falls within the critical region and thus make a decision about the null hypothesis \(H_0\).
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 5 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