Currently patrons at the library speak at an average of 60 decibels. Will this average decline after the installation of a new computer plug in station? After the plug in station was built, the librarian randomly recorded 51 people speaking at the library. Their average decibel level was 57.8 and their standard deviation was 6. What can be concluded at the the a = 0.01 level of significance? a. For this study, we should use Select an answer b. The null and alternative hypotheses would be: Ho: ? H₁: ? Select an answer Select an answer o c. The test statistic ? C d. The p-value = 11 (please show your answer to 3 decimal places.) (Please show your answer to 4 decimal places
Currently patrons at the library speak at an average of 60 decibels. Will this average decline after the installation of a new computer plug in station? After the plug in station was built, the librarian randomly recorded 51 people speaking at the library. Their average decibel level was 57.8 and their standard deviation was 6. What can be concluded at the the a = 0.01 level of significance? a. For this study, we should use Select an answer b. The null and alternative hypotheses would be: Ho: ? H₁: ? Select an answer Select an answer o c. The test statistic ? C d. The p-value = 11 (please show your answer to 3 decimal places.) (Please show your answer to 4 decimal places
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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![### Hypothesis Testing for Decibel Levels in a Library
**Scenario:**
Currently, patrons at the library speak at an average of 60 decibels. Will this average decline after the installation of a new computer plug-in station? After the plug-in station was built, the librarian randomly recorded 51 people speaking at the library. Their average decibel level was 57.8, and their standard deviation was 6. What can be concluded at the \(\alpha = 0.01\) level of significance?
**Steps for Hypothesis Testing:**
a. **Select the Appropriate Test:**
- Choose the appropriate statistical test based on the context.
b. **State the Null and Alternative Hypotheses:**
- **\(H_0\):** The null hypothesis is that the average decibel level is equal to 60 (no change).
- **\(H_1\):** The alternative hypothesis is that the average decibel level is less than 60 (a decrease).
c. **Calculate the Test Statistic:**
- Compute the test statistic using the formula:
\[
z = \frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}}}
\]
- \(\bar{x} = 57.8\), \(\mu = 60\), \(\sigma = 6\), \(n = 51\).
d. **Find the p-value:**
- Calculate the p-value corresponding to the test statistic.
e. **Compare the p-value and Significance Level:**
- Check if \( p \leq \alpha \).
f. **Make a Decision:**
- Decide whether to reject or fail to reject the null hypothesis based on the p-value.
g. **Conclude:**
- Make a conclusion based on the decision.
- Options for conclusion:
- The data suggest the population mean has not significantly decreased from 60 at \(\alpha = 0.01\).
- There is statistically significant evidence to conclude that the population mean has decreased since the plug-in station was built.
**Hint:**
- Utilize the provided links for calculation help, setup guidance, and interpretations.
This exercise involves inferential statistics to determine if a change in the environment affects average loudness in the library, using hypothesis testing at a given significance level.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F16eaad05-c857-4f7c-933f-0b1cc2121bed%2Fbd7d792e-96cf-4f1f-b12b-33ab3b962e70%2F4u4rypf_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Hypothesis Testing for Decibel Levels in a Library
**Scenario:**
Currently, patrons at the library speak at an average of 60 decibels. Will this average decline after the installation of a new computer plug-in station? After the plug-in station was built, the librarian randomly recorded 51 people speaking at the library. Their average decibel level was 57.8, and their standard deviation was 6. What can be concluded at the \(\alpha = 0.01\) level of significance?
**Steps for Hypothesis Testing:**
a. **Select the Appropriate Test:**
- Choose the appropriate statistical test based on the context.
b. **State the Null and Alternative Hypotheses:**
- **\(H_0\):** The null hypothesis is that the average decibel level is equal to 60 (no change).
- **\(H_1\):** The alternative hypothesis is that the average decibel level is less than 60 (a decrease).
c. **Calculate the Test Statistic:**
- Compute the test statistic using the formula:
\[
z = \frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}}}
\]
- \(\bar{x} = 57.8\), \(\mu = 60\), \(\sigma = 6\), \(n = 51\).
d. **Find the p-value:**
- Calculate the p-value corresponding to the test statistic.
e. **Compare the p-value and Significance Level:**
- Check if \( p \leq \alpha \).
f. **Make a Decision:**
- Decide whether to reject or fail to reject the null hypothesis based on the p-value.
g. **Conclude:**
- Make a conclusion based on the decision.
- Options for conclusion:
- The data suggest the population mean has not significantly decreased from 60 at \(\alpha = 0.01\).
- There is statistically significant evidence to conclude that the population mean has decreased since the plug-in station was built.
**Hint:**
- Utilize the provided links for calculation help, setup guidance, and interpretations.
This exercise involves inferential statistics to determine if a change in the environment affects average loudness in the library, using hypothesis testing at a given significance level.
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