### Analysis of Accident Rates at Controlled IntersectionsThe average number of accidents at controlled intersections per year is 5.4. We are examining if this average is higher for intersections with cameras installed. In a sample of 47 intersections with cameras, the observed average was 5.9 accidents per year with a standard deviation of 1.08. The analysis is conducted at a 0.01 level of significance.#### Steps for the Analysis:a. **Test Type Selection** - Choose the appropriate test for analysis.b. **Hypothesis Setup** - Null Hypothesis ($H_0$): The average is 5.4 accidents per year. - Alternative Hypothesis ($H_1$): The average is more than 5.4 accidents per year.c. **Calculate the Test Statistic** - Compute the test statistic to three decimal places.d. **Determine the p-value** - Compute the p-value to four decimal places.e. **Compare p-value with Significance Level ($\alpha$)** - Assess whether the p-value is less than $\alpha = 0.01$.f. **Decision on Null Hypothesis** - Decide whether to reject or fail to reject the null hypothesis.g. **Conclusion** - Based on the analysis, conclude whether the average number of accidents is significantly higher at intersections with cameras.h. **Interpret p-value Contextually** - Explanation of the p-value in the context of the study, assessing Type I error risk.#### Conclusion Options:1. **Significant Increase** - The data indicate that the population mean is significantly more than 5.4, providing substantial evidence that intersections with cameras have more than 5.4 accidents per year.2. **No Significant Increase** - The data suggest no significant increase beyond 5.4, indicating insufficient evidence for a higher accident mean at intersections with cameras.3. **Sample Mean Analysis** - Evaluates if the sample mean significantly differs from 5.9, assessing specific sample characteristics rather than population inference.#### Contextual Interpretation:- Explain statistical error risks, particularly the potential of a Type I error (incorrect rejection of a true null hypothesis).- Discuss implications if the population accident mean is indeed higher or matches 5.4 under observation of similar intersection samples.This analysis guides understanding whether traffic cameras at intersections correlate with accident rates, and whether observed differences are statistically The document provides questions related to statistical analysis in the context of a study on traffic accidents:h. Interpret the p-value in the context of the study.- There is a 0.13407982% chance that the population mean number of accidents per year at intersections with cameras installed is greater than 5.4.- There is a 0.13407982% chance of a Type I error.- If the population mean number of accidents per year at intersections with cameras installed is 5.4 and if another 47 intersections with cameras installed are observed, then there would be a 0.13407982% chance that the population mean number of accidents per year at intersections with cameras installed would be greater than 5.4.- If the population mean number of accidents per year at intersections with cameras installed is 5.4 and if another 47 intersections with cameras installed are observed, then there would be a 0.13407982% chance that the sample mean for these 47 intersections with cameras installed would be greater than 5.9.i. Interpret the level of significance in the context of the study.- If the population mean number of accidents per year at intersections with cameras installed is 5.4 and if another 47 intersections with cameras installed are observed, then there would be a 1% chance that we would end up falsely concluding that the population mean number of accidents per year at intersections with cameras installed is more than 5.4.- If the population mean number of accidents per year at intersections with cameras installed is more than 5.4 and if another 47 intersections with cameras installed are observed, then there would be a 1% chance that we would end up falsely concluding that the population mean number of accidents per year at intersections with cameras installed is equal to 5.4.- There is a 1% chance that you will get in a car accident, so please wear a seat belt.- There is a 1% chance that the population mean number of accidents per year at intersections with cameras installed is more than 5.4.

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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

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please answer d, e, f
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Does the average Presbyterian donate a different amount of money compared to the average Catholic in church on Sundays? The 55 randomly observed members of the Presbyterian church donated an average of $23 with a standard deviation of $6. The 41 randomly observed members of the Catholic church donated an average of $25 with a standard deviation of $10. What can be concluded at the a = 0.01 level of significance? a. For this study, we should use Select an answer b. The null and alternative hypotheses would be: Ho: Select an answer v Select an answer v Selec r v (please enter a decimal) an answe Hị: Select an answer vSelect an answer v Select an answer v (Please enter a decimal) c. The test statistic (please show your answer to 3 decimal places.) d. The p-value = e. The p-value is ? -a f. Based on this, we should Select an answer v the null hypothesis. g. Thus, the final conclusion is that ... (Please show your answer to 4 decimal places.) O The results are statistically significant at a…
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