nean smaller for houses owned by teachers? The data how the results of a survey of 16 teachers who were sked how many paintings they have in their houses. Assume that the distribution of the population is normal. , 10, 6, 9, 10, 6, 8, 10, 10, 8, 7, 9, 7, 8, 9, 8 What can be concluded at the a = 0.05 level of ignificance? a. For this study, we should use t-test for a population mean b. The null and alternative hypotheses would be: Ho: ? ☺ Select an answer
nean smaller for houses owned by teachers? The data how the results of a survey of 16 teachers who were sked how many paintings they have in their houses. Assume that the distribution of the population is normal. , 10, 6, 9, 10, 6, 8, 10, 10, 8, 7, 9, 7, 8, 9, 8 What can be concluded at the a = 0.05 level of ignificance? a. For this study, we should use t-test for a population mean b. The null and alternative hypotheses would be: Ho: ? ☺ Select an answer
MATLAB: An Introduction with Applications
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ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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![### Statistical Analysis of the Number of Paintings in Houses Owned by Teachers
The goal of this study is to determine whether the mean number of paintings in houses owned by teachers is smaller than the average of 9 paintings per house. A survey was conducted among 16 teachers to gather data on how many paintings they have in their houses. Below are the collected data points and the detailed analysis process.
#### Collected Data:
The number of paintings in each of the 16 surveyed teachers' houses is as follows:
```
9, 10, 6, 9, 10, 6, 8, 10, 10, 8, 7, 9, 7, 8, 9, 8
```
Given this data, we aim to draw a conclusion at a significance level of \( \alpha = 0.05 \).
#### Analytical Approach:
**a. Selection of Test:**
For this analysis, the appropriate test is:
- **t-test for a population mean**
**b. Hypotheses Formulation:**
- **Null Hypothesis (\(H_0\))**:
\[
H_0: \mu = 9
\]
(The mean number of paintings in houses owned by teachers is equal to the average of 9 paintings.)
- **Alternative Hypothesis (\(H_1\))**:
\[
H_1: \mu < 9
\]
(The mean number of paintings in houses owned by teachers is less than the average of 9 paintings.)
**c. Test Statistic:**
The test statistic for this analysis is denoted as \( t \), and the value is calculated using the sample data.
\[
t = \frac{\bar{X} - \mu}{\frac{s}{\sqrt{n}}}
\]
where:
- \(\bar{X}\) is the sample mean
- \(\mu\) is the population mean (9 in this case)
- \(s\) is the sample standard deviation
- \(n\) is the sample size (16 in this case)
Please show your answer to 3 decimal places.
**d. P-value:**
The p-value needs to be calculated based on the test statistic \( t \). This will help determine the probability of observing the sample data under the null hypothesis.
Please show your answer to 4 decimal places.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc2d30e49-de0d-418d-b702-a4b3e53b4c91%2Faabb0197-2bd8-4e26-8bf9-0887c14733be%2F5xffp9_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Statistical Analysis of the Number of Paintings in Houses Owned by Teachers
The goal of this study is to determine whether the mean number of paintings in houses owned by teachers is smaller than the average of 9 paintings per house. A survey was conducted among 16 teachers to gather data on how many paintings they have in their houses. Below are the collected data points and the detailed analysis process.
#### Collected Data:
The number of paintings in each of the 16 surveyed teachers' houses is as follows:
```
9, 10, 6, 9, 10, 6, 8, 10, 10, 8, 7, 9, 7, 8, 9, 8
```
Given this data, we aim to draw a conclusion at a significance level of \( \alpha = 0.05 \).
#### Analytical Approach:
**a. Selection of Test:**
For this analysis, the appropriate test is:
- **t-test for a population mean**
**b. Hypotheses Formulation:**
- **Null Hypothesis (\(H_0\))**:
\[
H_0: \mu = 9
\]
(The mean number of paintings in houses owned by teachers is equal to the average of 9 paintings.)
- **Alternative Hypothesis (\(H_1\))**:
\[
H_1: \mu < 9
\]
(The mean number of paintings in houses owned by teachers is less than the average of 9 paintings.)
**c. Test Statistic:**
The test statistic for this analysis is denoted as \( t \), and the value is calculated using the sample data.
\[
t = \frac{\bar{X} - \mu}{\frac{s}{\sqrt{n}}}
\]
where:
- \(\bar{X}\) is the sample mean
- \(\mu\) is the population mean (9 in this case)
- \(s\) is the sample standard deviation
- \(n\) is the sample size (16 in this case)
Please show your answer to 3 decimal places.
**d. P-value:**
The p-value needs to be calculated based on the test statistic \( t \). This will help determine the probability of observing the sample data under the null hypothesis.
Please show your answer to 4 decimal places.
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