A survey of 62 men found that 12 have a social media account. Another survey of 57 women found that 40 have a social media account. Is the percentage of women that have a social media account more than men based on a-level of 0.07?
A survey of 62 men found that 12 have a social media account. Another survey of 57 women found that 40 have a social media account. Is the percentage of women that have a social media account more than men based on a-level of 0.07?
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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A survey of 62 men found that 12 have a social media account. Another survey of 57 women found that 40 have a social media account. Is the percentage of women that have a social media account more than men based on a-level of 0.07?
![**Finding Critical Values and Test Formulas**
---
**c) To find our Critical Value(s) (CV), will we use invNorm(), invT()?**
- [Dropdown: Select an answer]
**d) Please explain the reason for the correct answer for step c.**
- [Dropdown: Select an answer]
**Round to Two Decimal Places**
CV = [Input box]
---
**f) What formula will we use for the test value?**
1. \( z = \frac{\hat{p} - p}{\sqrt{\frac{pq}{n}}} \)
2. \( z = \frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}}} \)
3. \( t = \frac{(\bar{x}_1 - \bar{x}_2) - (\mu_1 - \mu_2)}{\sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}}} \)
4. \( z = \frac{(\hat{p}_1 - \hat{p}_2) - (p_1 - p_2)}{\sqrt{\hat{p} \cdot \hat{q} \cdot \left( \frac{1}{n_1} + \frac{1}{n_2} \right)}} \)
5. \( t = \frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}}} \)
---
**Explanation of Formulas:**
- **Formula 1:** A z-test for a sample proportion. It uses the sample proportion \(\hat{p}\), the population proportion \(p\), and the standard error based on \(pq/n\).
- **Formula 2:** A z-test for a sample mean with a known population standard deviation \(\sigma\).
- **Formula 3:** A t-test for the difference between two sample means with unknown population standard deviations, uses \(s_1\) and \(s_2\) for sample standard deviations.
- **Formula 4:** A z-test for the difference between two sample proportions.
- **Formula 5:** A t-test for a sample mean with an unknown population standard deviation, using the sample standard deviation \(s\).
Use the dropdowns and input boxes to complete the questions and provide calculations.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Faa466c24-bbae-451a-a078-10dcd226e22a%2F098becdb-fab4-41f3-96d5-3cb4a3282a52%2Fq0y7fsd.jpeg&w=3840&q=75)
Transcribed Image Text:**Finding Critical Values and Test Formulas**
---
**c) To find our Critical Value(s) (CV), will we use invNorm(), invT()?**
- [Dropdown: Select an answer]
**d) Please explain the reason for the correct answer for step c.**
- [Dropdown: Select an answer]
**Round to Two Decimal Places**
CV = [Input box]
---
**f) What formula will we use for the test value?**
1. \( z = \frac{\hat{p} - p}{\sqrt{\frac{pq}{n}}} \)
2. \( z = \frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}}} \)
3. \( t = \frac{(\bar{x}_1 - \bar{x}_2) - (\mu_1 - \mu_2)}{\sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}}} \)
4. \( z = \frac{(\hat{p}_1 - \hat{p}_2) - (p_1 - p_2)}{\sqrt{\hat{p} \cdot \hat{q} \cdot \left( \frac{1}{n_1} + \frac{1}{n_2} \right)}} \)
5. \( t = \frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}}} \)
---
**Explanation of Formulas:**
- **Formula 1:** A z-test for a sample proportion. It uses the sample proportion \(\hat{p}\), the population proportion \(p\), and the standard error based on \(pq/n\).
- **Formula 2:** A z-test for a sample mean with a known population standard deviation \(\sigma\).
- **Formula 3:** A t-test for the difference between two sample means with unknown population standard deviations, uses \(s_1\) and \(s_2\) for sample standard deviations.
- **Formula 4:** A z-test for the difference between two sample proportions.
- **Formula 5:** A t-test for a sample mean with an unknown population standard deviation, using the sample standard deviation \(s\).
Use the dropdowns and input boxes to complete the questions and provide calculations.
Transcribed Image Text:**Title: Statistical Proportions and Normal Distribution**
**Instructions:**
Write as a Decimal Rounded to Two Decimal Places
**Inputs Required:**
- **Sample Proportion Women**: Enter the value here (use two decimal places).
- **Sample Proportion Men**: Enter the value here (use two decimal places).
**Selection:**
- Choose an appropriate answer from the dropdown menu provided.
**Further Calculations:**
- Two unspecified values require inputs:
1. Enter a value here.
2. Enter a value here.
- **Sample Size Women**: Enter the sample size (use two decimal places).
- **Sample Size Men**: Enter the sample size (use two decimal places).
**Final Calculation:**
- **Round to Two Decimal Places**: Enter the final calculated value here.
**Question:**
h) Please select the option that best represents where the test value will be located on the correct normal distribution curve.
This exercise guides you through determining sample proportions and sizes, and involves selecting a response based on statistical distribution.
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