mple random sample of size n=40 is drawn from a population. The sample mean i found to be 102.8, and the sample standard deviation is found to be 15.7. Is the population in greater than 100 at the a=0.10 level of significance? CEE termine the null and alternative hypotheses. 5² μ=100 1. H> 100 Compute the test statistic (Round to two decimal places as needed.)
mple random sample of size n=40 is drawn from a population. The sample mean i found to be 102.8, and the sample standard deviation is found to be 15.7. Is the population in greater than 100 at the a=0.10 level of significance? CEE termine the null and alternative hypotheses. 5² μ=100 1. H> 100 Compute the test statistic (Round to two decimal places as needed.)
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
![Title: Statistical Hypothesis Testing
---
**Problem Statement:**
A simple random sample of size n = 40 is drawn from a population. The sample mean is found to be 102.8, and the sample standard deviation is found to be 15.7. Is the population mean greater than 100 at the α = 0.10 level of significance?
---
**Step 1: Formulate Hypotheses**
To address this question, we need to establish our null and alternative hypotheses:
- **Null Hypothesis (H₀):** μ = 100
- **Alternative Hypothesis (H₁):** μ > 100
Here, μ denotes the population mean.
---
**Step 2: Compute the Test Statistic**
To determine if the population mean is statistically greater than 100, we need to calculate the test statistic using the sample data. The test statistic formula often used is:
\[
t = \frac{\bar{x} - \mu_0}{\frac{s}{\sqrt{n}}}
\]
where:
- \(\bar{x}\) is the sample mean (102.8)
- μ₀ is the population mean under the null hypothesis (100)
- s is the sample standard deviation (15.7)
- n is the sample size (40)
The detailed computation is omitted for brevity here, but the interface highlights the need to round to two decimal places as needed.
---
**Step 3: Decision Rule**
Compare the computed test statistic to the critical value from the t-distribution table at the 0.10 level of significance for a one-tailed test. The degrees of freedom (df) for this test are \( n - 1 = 40 - 1 = 39 \).
---
**Interface Options:**
The educational tool offers the following aids:
- **Help me solve this**
- **View an example**
- **Get more help**
These options can guide students through the problem-solving process interactively.
---
**Additional Options:**
- Buttons for clearing the response: **Clear all**
- Button to check the submitted answer: **Check answer**
---
**Note:**
The screenshot shows a user interface designed to facilitate learning through interactive question-solving. The Python environment and other computational tools can be used to perform the necessary calculations and validate the hypotheses.
**Screenshot Analysis:**
The laptop screen captures part of a software interface that aids in hypothesis testing. The problem shown involves statistical](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcfee5922-5e9b-4d5c-bb5d-6eee324be123%2Fe9ce7482-537a-47d7-bf95-c7ccc6ba00f8%2Ff9iuh1_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Title: Statistical Hypothesis Testing
---
**Problem Statement:**
A simple random sample of size n = 40 is drawn from a population. The sample mean is found to be 102.8, and the sample standard deviation is found to be 15.7. Is the population mean greater than 100 at the α = 0.10 level of significance?
---
**Step 1: Formulate Hypotheses**
To address this question, we need to establish our null and alternative hypotheses:
- **Null Hypothesis (H₀):** μ = 100
- **Alternative Hypothesis (H₁):** μ > 100
Here, μ denotes the population mean.
---
**Step 2: Compute the Test Statistic**
To determine if the population mean is statistically greater than 100, we need to calculate the test statistic using the sample data. The test statistic formula often used is:
\[
t = \frac{\bar{x} - \mu_0}{\frac{s}{\sqrt{n}}}
\]
where:
- \(\bar{x}\) is the sample mean (102.8)
- μ₀ is the population mean under the null hypothesis (100)
- s is the sample standard deviation (15.7)
- n is the sample size (40)
The detailed computation is omitted for brevity here, but the interface highlights the need to round to two decimal places as needed.
---
**Step 3: Decision Rule**
Compare the computed test statistic to the critical value from the t-distribution table at the 0.10 level of significance for a one-tailed test. The degrees of freedom (df) for this test are \( n - 1 = 40 - 1 = 39 \).
---
**Interface Options:**
The educational tool offers the following aids:
- **Help me solve this**
- **View an example**
- **Get more help**
These options can guide students through the problem-solving process interactively.
---
**Additional Options:**
- Buttons for clearing the response: **Clear all**
- Button to check the submitted answer: **Check answer**
---
**Note:**
The screenshot shows a user interface designed to facilitate learning through interactive question-solving. The Python environment and other computational tools can be used to perform the necessary calculations and validate the hypotheses.
**Screenshot Analysis:**
The laptop screen captures part of a software interface that aids in hypothesis testing. The problem shown involves statistical
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 1 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