A hot topic of debate is whether the legal driving age should be raised to eighteen. From a random sample of 400 Americans, 52% favored raising the legal driving age to eighteen. Based on the data, can you conclude that a majority of Americans believe the legal driving age should be raised to 18? Let a = 2.5%
A hot topic of debate is whether the legal driving age should be raised to eighteen. From a random sample of 400 Americans, 52% favored raising the legal driving age to eighteen. Based on the data, can you conclude that a majority of Americans believe the legal driving age should be raised to 18? Let a = 2.5%
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 Public Opinion on Raising the Legal Driving Age
**Question 22:**
A hot topic of debate is whether the legal driving age should be raised to eighteen. From a random sample of 400 Americans, 52% favored raising the legal driving age to eighteen. Based on the data, can you conclude that a majority of Americans believe the legal driving age should be raised to 18?
*Let \( \alpha = 2.5\% \)*
**Analysis:**
To determine whether a majority of Americans favor raising the legal driving age to 18, we perform a hypothesis test on the population proportion. Here's how we can approach this analysis:
1. **Define Hypotheses**:
- Null Hypothesis (\(H_0\)): \( p = 0.5 \) (The proportion of Americans who favor raising the driving age is 50%.)
- Alternative Hypothesis (\(H_1\)): \( p > 0.5 \) (The proportion of Americans who favor raising the driving age is greater than 50%.)
2. **Calculate Test Statistic**:
Using the sample proportion (\(\hat{p} = 0.52\)), sample size (n = 400), and population proportion under the null hypothesis (\(p_0 = 0.5\)), the test statistic for a proportion is:
\[
Z = \frac{\hat{p} - p_0}{\sqrt{\frac{p_0 (1 - p_0)}{n}}}
\]
3. **Compute P-Value**:
After finding the Z value, compare it against a standard normal distribution to find the p-value.
4. **Compare with Significance Level**:
If the p-value is less than the significance level (\(\alpha = 0.025\)), reject the null hypothesis. Otherwise, do not reject the null hypothesis.
**Conclusion**:
The decision from the hypothesis test will indicate whether there is sufficient evidence to conclude that a majority of Americans favor raising the legal driving age to 18.
This approach allows us to determine the public opinion on this important issue using statistical methods.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F13ae00e5-d197-4a7b-bd80-139c55aabc36%2F1c6f37ee-cc8c-4f0a-9925-94f0c2da4fad%2Fb0ztj6h.jpeg&w=3840&q=75)
Transcribed Image Text:### Statistical Analysis of Public Opinion on Raising the Legal Driving Age
**Question 22:**
A hot topic of debate is whether the legal driving age should be raised to eighteen. From a random sample of 400 Americans, 52% favored raising the legal driving age to eighteen. Based on the data, can you conclude that a majority of Americans believe the legal driving age should be raised to 18?
*Let \( \alpha = 2.5\% \)*
**Analysis:**
To determine whether a majority of Americans favor raising the legal driving age to 18, we perform a hypothesis test on the population proportion. Here's how we can approach this analysis:
1. **Define Hypotheses**:
- Null Hypothesis (\(H_0\)): \( p = 0.5 \) (The proportion of Americans who favor raising the driving age is 50%.)
- Alternative Hypothesis (\(H_1\)): \( p > 0.5 \) (The proportion of Americans who favor raising the driving age is greater than 50%.)
2. **Calculate Test Statistic**:
Using the sample proportion (\(\hat{p} = 0.52\)), sample size (n = 400), and population proportion under the null hypothesis (\(p_0 = 0.5\)), the test statistic for a proportion is:
\[
Z = \frac{\hat{p} - p_0}{\sqrt{\frac{p_0 (1 - p_0)}{n}}}
\]
3. **Compute P-Value**:
After finding the Z value, compare it against a standard normal distribution to find the p-value.
4. **Compare with Significance Level**:
If the p-value is less than the significance level (\(\alpha = 0.025\)), reject the null hypothesis. Otherwise, do not reject the null hypothesis.
**Conclusion**:
The decision from the hypothesis test will indicate whether there is sufficient evidence to conclude that a majority of Americans favor raising the legal driving age to 18.
This approach allows us to determine the public opinion on this important issue using statistical methods.
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