MATLAB: An Introduction with Applications
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ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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![**17. Survey on Government Restrictions on Food and Drink Choices**
One of the hot topics in the last presidential election was related to our citizens' health and whether or not the government has the right to limit our choices in what we eat or drink. A random sample of 1,046 Americans was obtained. The question asked was, "Do you support our government banning specific types or sizes of food or drinks?" Of those surveyed, 895 responded, "no."
a. **Estimate with 95% Confidence the Proportion of Americans who do not support the Government Banning Specific Types or Sizes of Food or Drinks:**
To estimate the proportion with 95% confidence, we use the formula for the confidence interval for a population proportion:
- Sample size (n) = 1,046
- Number of people who said "no" (x) = 895
- Sample proportion (p-hat) = x/n = 895/1046
Using the standard error formula for the proportion and the Z-score for 95% confidence (which is typically 1.96), we will calculate the confidence interval.
b. **Using the Confidence Interval Found in Part a, Can You Conclude that a Majority of Americans Do Not Support the Government Banning Specific Types of Sizes of Food or Drinks? Why or Why Not:**
To determine whether the majority (more than 50% of the population) do not support the government's banning of specific types or sizes of food or drinks, we need to see if the entire confidence interval lies above 0.50 (50%).
**Steps for Calculations:**
1. Calculate the sample proportion (p-hat) = 895 / 1046
2. Find the standard error (SE) = sqrt[ (p-hat * (1 - p-hat)) / n ]
3. Calculate the margin of error (ME) = Z * SE, where Z = 1.96 for 95% confidence
4. Find the confidence interval: p-hat ± ME
**Interpretation:**
If the confidence interval does not include 0.50 and is entirely above it, we can conclude with 95% confidence that a majority of Americans do not support such government bans. If it includes 0.50, we cannot make a definitive conclusion regarding the majority stance.
These calculations reveal important insights into the public opinion on government intervention in citizens' dietary choices, reflecting broader implications for](https://content.bartleby.com/qna-images/question/13ae00e5-d197-4a7b-bd80-139c55aabc36/b1e64409-5af7-49da-ad74-60604f357679/f5fpb4d.jpeg)
Transcribed Image Text:**17. Survey on Government Restrictions on Food and Drink Choices**
One of the hot topics in the last presidential election was related to our citizens' health and whether or not the government has the right to limit our choices in what we eat or drink. A random sample of 1,046 Americans was obtained. The question asked was, "Do you support our government banning specific types or sizes of food or drinks?" Of those surveyed, 895 responded, "no."
a. **Estimate with 95% Confidence the Proportion of Americans who do not support the Government Banning Specific Types or Sizes of Food or Drinks:**
To estimate the proportion with 95% confidence, we use the formula for the confidence interval for a population proportion:
- Sample size (n) = 1,046
- Number of people who said "no" (x) = 895
- Sample proportion (p-hat) = x/n = 895/1046
Using the standard error formula for the proportion and the Z-score for 95% confidence (which is typically 1.96), we will calculate the confidence interval.
b. **Using the Confidence Interval Found in Part a, Can You Conclude that a Majority of Americans Do Not Support the Government Banning Specific Types of Sizes of Food or Drinks? Why or Why Not:**
To determine whether the majority (more than 50% of the population) do not support the government's banning of specific types or sizes of food or drinks, we need to see if the entire confidence interval lies above 0.50 (50%).
**Steps for Calculations:**
1. Calculate the sample proportion (p-hat) = 895 / 1046
2. Find the standard error (SE) = sqrt[ (p-hat * (1 - p-hat)) / n ]
3. Calculate the margin of error (ME) = Z * SE, where Z = 1.96 for 95% confidence
4. Find the confidence interval: p-hat ± ME
**Interpretation:**
If the confidence interval does not include 0.50 and is entirely above it, we can conclude with 95% confidence that a majority of Americans do not support such government bans. If it includes 0.50, we cannot make a definitive conclusion regarding the majority stance.
These calculations reveal important insights into the public opinion on government intervention in citizens' dietary choices, reflecting broader implications for
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