the standard deviation of test scores were students from school A is different from the standard deviation of test scores for students from school B. How many populations? 01 What is the parameter? O Difference between Means O Mean O ariance O Proportion O Standard Deviation
the standard deviation of test scores were students from school A is different from the standard deviation of test scores for students from school B. How many populations? 01 What is the parameter? O Difference between Means O Mean O ariance O Proportion O Standard Deviation
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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Transcribed Image Text:**Text and Explanation for Educational Website:**
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**Hypothesis Testing for Standard Deviation Differences**
Test scores for random samples of students from two different schools were recorded. We aim to test the claim that the standard deviation of test scores for students from School A is different from the standard deviation of test scores for students from School B.
**How many populations?**
- Option 1: 1
- Option 2: 2
In this scenario, we are dealing with two distinct populations: students from School A and students from School B.
**What is the parameter?**
- Option 1: Difference between Means
- Option 2: Mean
- Option 3: Variance
- Option 4: Proportion
- Option 5: Standard Deviation
The parameter of interest in this test is the **Standard Deviation**, as we are examining the claim concerning differences in variability (standard deviation) of test scores between the two schools.
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This text introduces a statistical test for comparing standard deviations between two groups, illustrating key concepts of hypothesis testing and parameter identification in statistics.
![The image presents a multiple-choice question titled "What is the test statistic?" with several mathematical formulas for different statistical tests. Here is the transcription of each option:
1. **Option A (z for proportions):**
\[
z = \frac{\hat{p} - p}{\sqrt{\frac{p \cdot q}{n}}}
\]
2. **Option B (F-test for variances):**
\[
F = \frac{s^2_1}{s^2_2}
\]
3. **Option C (z for means):**
\[
z = \frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}}}
\]
4. **Option D (z for two proportions):**
\[
z = \frac{(\hat{p_1} - \hat{p_2}) - (p_1 - p_2)}{\sqrt{\frac{p \cdot q}{n_1} + \frac{p \cdot q}{n_2}}}
\]
5. **Option E (t for sample mean):**
\[
t = \frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}}}
\]
6. **Option F (chi-squared test):**
\[
\chi^2 = \frac{(n-1)^2 \cdot s^2}{\sigma^2}
\]
7. **Option G (t for paired samples):**
\[
t_d = \frac{\bar{x} - \mu_d}{\frac{s_d}{\sqrt{n}}}
\]
8. **Option H (t for difference in means):**
\[
t = \frac{(\bar{x_1} - \bar{x_2}) - (\mu_1 - \mu_2)}{\sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}}}
\]
9. **Option I (t for unequal variances):**
\[
t = \frac{(\bar{x_1} - \bar{x_2}) - (\mu_1 - \mu_2)}{\sqrt{\frac{s_1^2}{n_1} +](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff9076e7a-57c1-402a-997f-53718f1a9a67%2F912847ad-814f-44b6-aef4-a8d56b6a90f6%2Fw7lhob_processed.png&w=3840&q=75)
Transcribed Image Text:The image presents a multiple-choice question titled "What is the test statistic?" with several mathematical formulas for different statistical tests. Here is the transcription of each option:
1. **Option A (z for proportions):**
\[
z = \frac{\hat{p} - p}{\sqrt{\frac{p \cdot q}{n}}}
\]
2. **Option B (F-test for variances):**
\[
F = \frac{s^2_1}{s^2_2}
\]
3. **Option C (z for means):**
\[
z = \frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}}}
\]
4. **Option D (z for two proportions):**
\[
z = \frac{(\hat{p_1} - \hat{p_2}) - (p_1 - p_2)}{\sqrt{\frac{p \cdot q}{n_1} + \frac{p \cdot q}{n_2}}}
\]
5. **Option E (t for sample mean):**
\[
t = \frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}}}
\]
6. **Option F (chi-squared test):**
\[
\chi^2 = \frac{(n-1)^2 \cdot s^2}{\sigma^2}
\]
7. **Option G (t for paired samples):**
\[
t_d = \frac{\bar{x} - \mu_d}{\frac{s_d}{\sqrt{n}}}
\]
8. **Option H (t for difference in means):**
\[
t = \frac{(\bar{x_1} - \bar{x_2}) - (\mu_1 - \mu_2)}{\sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}}}
\]
9. **Option I (t for unequal variances):**
\[
t = \frac{(\bar{x_1} - \bar{x_2}) - (\mu_1 - \mu_2)}{\sqrt{\frac{s_1^2}{n_1} +
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