Test the following claim. Make sure to include the critical value, a sketch of the critical value, and the test statistic. A simple random sample of weights of 19 green M&Ms has a mean of .8635 g. Assume that o =.0565 g. Use a .05 significance level to test the claim that the mean weight of all green M&Ms is less than 8435g, which is the mean weight printed on the label.
Test the following claim. Make sure to include the critical value, a sketch of the critical value, and the test statistic. A simple random sample of weights of 19 green M&Ms has a mean of .8635 g. Assume that o =.0565 g. Use a .05 significance level to test the claim that the mean weight of all green M&Ms is less than 8435g, which is the mean weight printed on the label.
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
Topic Video
Question

Transcribed Image Text:b) Provide the p-value of the above test.
![**Hypothesis Testing Problem**
**Objective:**
Test the following claim. Ensure to include the critical value, a sketch of the critical value, and the test statistic.
**Problem Statement:**
A simple random sample of weights of 19 green M&Ms has a mean weight of 0.8635 grams. Assume that the population standard deviation \( \sigma = 0.0565 \) grams. Use a 0.05 significance level to test the claim that the mean weight of all green M&Ms is less than 0.845 grams, which is the mean weight printed on the label.
**Solution Steps:**
1. **State the Null and Alternative Hypotheses:**
- Null Hypothesis (\( H_0 \)): The mean weight of green M&Ms is 0.845 grams.
- Alternative Hypothesis (\( H_a \)): The mean weight of green M&Ms is less than 0.845 grams.
2. **Determine the Significance Level:**
- Use a significance level (\( \alpha \)) of 0.05.
3. **Calculate the Test Statistic:**
- Use the z-test for hypothesis testing since the population standard deviation is known.
- The formula for the z-test statistic is:
\[
z = \frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}}}
\]
where \( \bar{x} \) is the sample mean, \( \mu \) is the population mean, \( \sigma \) is the standard deviation, and \( n \) is the sample size.
4. **Find the Critical Value:**
- Determine the critical value from the z-table for a one-tailed test at \( \alpha = 0.05 \).
5. **Sketch and Analyze:**
- Create a sketch showing the normal distribution curve, the critical region, and the location of the test statistic.
- Compare the test statistic to the critical value to determine whether to reject the null hypothesis.
6. **Conclusion:**
- Based on the comparison, conclude whether the mean weight of all green M&Ms is statistically less than 0.845 grams.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F06713f80-6d89-4ff3-92d9-3108122eed6b%2Ff83894ef-1285-400d-bd36-e4a604322c92%2Ftpfbd8_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Hypothesis Testing Problem**
**Objective:**
Test the following claim. Ensure to include the critical value, a sketch of the critical value, and the test statistic.
**Problem Statement:**
A simple random sample of weights of 19 green M&Ms has a mean weight of 0.8635 grams. Assume that the population standard deviation \( \sigma = 0.0565 \) grams. Use a 0.05 significance level to test the claim that the mean weight of all green M&Ms is less than 0.845 grams, which is the mean weight printed on the label.
**Solution Steps:**
1. **State the Null and Alternative Hypotheses:**
- Null Hypothesis (\( H_0 \)): The mean weight of green M&Ms is 0.845 grams.
- Alternative Hypothesis (\( H_a \)): The mean weight of green M&Ms is less than 0.845 grams.
2. **Determine the Significance Level:**
- Use a significance level (\( \alpha \)) of 0.05.
3. **Calculate the Test Statistic:**
- Use the z-test for hypothesis testing since the population standard deviation is known.
- The formula for the z-test statistic is:
\[
z = \frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}}}
\]
where \( \bar{x} \) is the sample mean, \( \mu \) is the population mean, \( \sigma \) is the standard deviation, and \( n \) is the sample size.
4. **Find the Critical Value:**
- Determine the critical value from the z-table for a one-tailed test at \( \alpha = 0.05 \).
5. **Sketch and Analyze:**
- Create a sketch showing the normal distribution curve, the critical region, and the location of the test statistic.
- Compare the test statistic to the critical value to determine whether to reject the null hypothesis.
6. **Conclusion:**
- Based on the comparison, conclude whether the mean weight of all green M&Ms is statistically less than 0.845 grams.
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 3 steps with 2 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.Similar questions
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