Approximately 51% of all fatal auto accidents are caused by driver error, according to the American Automobile Association. 40 randomly selected fatal accidents are examined, and it is determined that 15 were caused by driver error. Using a = 0.10, is the AAA proportion accurate? Round to 3 decimal places, unless asked otherwise. a. The null hypothesis is p> 0.51 (write 'true" or "false" in the blank): b. The value of p-hat is c. The value of the test-statistic is

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### Analysis of Proportion of Fatal Auto Accidents Caused by Driver Error

According to the American Automobile Association, approximately 51% of all fatal auto accidents are caused by driver error. To verify this claim, a sample of 40 randomly selected fatal accidents was examined, and it was determined that 15 of these were caused by driver error. Utilizing a significance level \(\alpha = 0.10\), we aim to determine whether the AAA's proportion is accurate. Perform the following calculations rounding to three decimal places unless otherwise specified.

#### Steps for Hypothesis Testing:

a. **Null Hypothesis (H0)**: The null hypothesis states that the proportion \( p \) of fatal auto accidents caused by driver error is greater than 0.51. 
   - Answer provided should be either "true" or "false":  `_______`

b. **Sample Proportion (\(\hat{p}\))**: The observed proportion of fatal accidents in the sample caused by driver error is calculated as follows:
   - \(\hat{p}\) = \(\dfrac{\text{Number of accidents caused by driver error}}{\text{Total number of accidents in sample}}\)
   - Insert the calculated value into the blank:  `_______`

c. **Test Statistic**: The test statistic for a proportion is calculated using the formula:
   - \(z = \dfrac{\hat{p} - p}{\sqrt{\dfrac{p(1 - p)}{n}}}\)
   - Where \(p\) is the population proportion, \(\hat{p}\) is the sample proportion, and \(n\) is the sample size.
   - Insert the value of the test statistic into the blank:  `_______`

d. **Final Decision**: Based on the calculated test statistic and the significance level (\(\alpha = 0.10\)), decide whether to reject the null hypothesis.
   - If the test statistic falls in the critical region, reject \( H0 \). 
   - Answer provided should be either "true" or "false":  `_______`

---
Ensure to calculate each value accurately and compare the test statistic with the critical value for the given significance level to make the final decision.
Transcribed Image Text:### Analysis of Proportion of Fatal Auto Accidents Caused by Driver Error According to the American Automobile Association, approximately 51% of all fatal auto accidents are caused by driver error. To verify this claim, a sample of 40 randomly selected fatal accidents was examined, and it was determined that 15 of these were caused by driver error. Utilizing a significance level \(\alpha = 0.10\), we aim to determine whether the AAA's proportion is accurate. Perform the following calculations rounding to three decimal places unless otherwise specified. #### Steps for Hypothesis Testing: a. **Null Hypothesis (H0)**: The null hypothesis states that the proportion \( p \) of fatal auto accidents caused by driver error is greater than 0.51. - Answer provided should be either "true" or "false": `_______` b. **Sample Proportion (\(\hat{p}\))**: The observed proportion of fatal accidents in the sample caused by driver error is calculated as follows: - \(\hat{p}\) = \(\dfrac{\text{Number of accidents caused by driver error}}{\text{Total number of accidents in sample}}\) - Insert the calculated value into the blank: `_______` c. **Test Statistic**: The test statistic for a proportion is calculated using the formula: - \(z = \dfrac{\hat{p} - p}{\sqrt{\dfrac{p(1 - p)}{n}}}\) - Where \(p\) is the population proportion, \(\hat{p}\) is the sample proportion, and \(n\) is the sample size. - Insert the value of the test statistic into the blank: `_______` d. **Final Decision**: Based on the calculated test statistic and the significance level (\(\alpha = 0.10\)), decide whether to reject the null hypothesis. - If the test statistic falls in the critical region, reject \( H0 \). - Answer provided should be either "true" or "false": `_______` --- Ensure to calculate each value accurately and compare the test statistic with the critical value for the given significance level to make the final decision.
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