A study conducted by Pugh Research found 68.7% of Americans do not want President Biden to seek re-election. In a random sample of 750 Americans, what is the likelihood at least 70% do not want President Biden to seek re-election?
A study conducted by Pugh Research found 68.7% of Americans do not want President Biden to seek re-election. In a random sample of 750 Americans, what is the likelihood at least 70% do not want President Biden to seek re-election?
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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Question 10 - Bayes’ Theorem
Please solve the problem with simple probability rules
Transcribed Image Text:**Example Problem: Probability Scenario**
A study conducted by Pugh Research found 68.7% of Americans do not want President Biden to seek re-election. In a random sample of 750 Americans, what is the likelihood that at least 70% do not want President Biden to seek re-election?
### Key Points to Consider:
**Proportion of Interest (p):** 68.7% or 0.687
**Sample Size (n):** 750
**Target Proportion (p0):** 70% or 0.700
**Objective:**
Determine the likelihood that at least 70% of the sample of 750 Americans do not want President Biden to seek re-election. This calculation involves determining the sampling distribution and applying it to the given scenario.
### Steps to Approach:
1. **Calculate the Mean (μ) of the Sampling Distribution:**
```
μ = p = 0.687
```
2. **Calculate the Standard Deviation (σ) of the Sampling Distribution:**
```
σ = sqrt( (p * (1 - p)) / n )
```
Substituting the values:
```
σ = sqrt( (0.687 * (1 - 0.687)) / 750 )
```
3. **Convert the Target Proportion to the Z-Score:**
The z-score formula is:
```
Z = (p0 - μ) / σ
```
4. **Find the Corresponding Probability:**
Using statistical tables or software to find the probability corresponding to the calculated z-score.
### Educational Objective:
Through this example, students can learn about the use of sampling distributions, hypothesis testing, and how to perform statistical calculations related to population proportions. This scenario integrates real-world data to emphasize the practical application of statistical concepts.
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