Data on the numbers of hospital admissions resulting from motor vehicle crashes are given below for Fridays on the 6th of a month and Fridays on the following 13th of the same month. Assume that the paired sample data is a simple random sample and that the differences have a distribution that is approximately normal. Construct a 95% confidence interval estimate of the mean of the population of differences between hospital admissions. Use the confidence interval to test the claim that when the 13th day of a month falls on a Friday, the numbers of hospital admissions from motor vehicle crashes are not affected. Friday the 6th 12 10 8 Friday the 13th 10 10 14 13 14 In this example, Ha is the mean value of the differences d for the population of all pairs of data, where each individual difference d is defined as the number of hospital admissions on Friday the 6th minus the number of hospital admissions on Friday the 13th. Find the 95% confidence interval (Round to two decimal places as needed.) Based on the confidence interval, can one reject the claim that when the 13th day of a month falls on a Friday, the numbers of hospital admissions from motor vehicle crashes are not affected? O A. Yes, because the confidence interval includes zero O B. No, because the confidence interval includes zero. O C. No, because the confidence interval does not include zero. O D. Yes, because the confidence interval does not include zero
Data on the numbers of hospital admissions resulting from motor vehicle crashes are given below for Fridays on the 6th of a month and Fridays on the following 13th of the same month. Assume that the paired sample data is a simple random sample and that the differences have a distribution that is approximately normal. Construct a 95% confidence interval estimate of the mean of the population of differences between hospital admissions. Use the confidence interval to test the claim that when the 13th day of a month falls on a Friday, the numbers of hospital admissions from motor vehicle crashes are not affected. Friday the 6th 12 10 8 Friday the 13th 10 10 14 13 14 In this example, Ha is the mean value of the differences d for the population of all pairs of data, where each individual difference d is defined as the number of hospital admissions on Friday the 6th minus the number of hospital admissions on Friday the 13th. Find the 95% confidence interval (Round to two decimal places as needed.) Based on the confidence interval, can one reject the claim that when the 13th day of a month falls on a Friday, the numbers of hospital admissions from motor vehicle crashes are not affected? O A. Yes, because the confidence interval includes zero O B. No, because the confidence interval includes zero. O C. No, because the confidence interval does not include zero. O D. Yes, because the confidence interval does not include zero
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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![**Educational Explanation: Confidence Intervals in Hospital Admissions Data**
In this example, we are analyzing data on the number of hospital admissions resulting from motor vehicle crashes. The data compares Fridays on the 6th of a month with Fridays on the 13th of the same month. The purpose is to determine if there is a significant difference in admissions when the 13th falls on a Friday, which some believe may be an "unlucky" day.
### Presented Data:
The table below shows the number of admissions for each date:
- **Friday the 6th:**
- 12, 5, 10, 8, 9
- **Friday the 13th:**
- 10, 14, 10, 14, 13
### Analysis:
The statistical measure we are using is the 95% confidence interval to estimate the mean of the population differences in admissions between these two dates. Each "difference" (d) is calculated as the admission number on Friday the 6th minus the admission number on Friday the 13th.
\[ \text{Mean difference (\( \mu_d \))} < \text{Mean of differences calculated} < \mu_d \]
**Note:** The exact bounds of the confidence interval should be calculated and rounded to two decimal places.
### Interpretation:
Based on this confidence interval, we need to evaluate whether we can reject the claim that hospital admissions are unaffected on Friday the 13th.
**Options:**
- **A.** Yes, because the confidence interval includes zero.
- **B.** No, since it includes zero, indicating no significant difference.
- **C.** No, because the interval does not include zero.
- **D.** Yes, because it does not include zero, indicating a significant difference.
The correct option will depend on the calculated confidence interval bounds.
This example illustrates how statistical tools, like confidence intervals, help in determining the likelihood of observed effects and guiding decision-making based on data analysis.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe4328229-d533-4b82-9231-8c3665946593%2F4a6cd9ea-f30e-422b-9107-3d4956b429bf%2Ft95cavt_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Educational Explanation: Confidence Intervals in Hospital Admissions Data**
In this example, we are analyzing data on the number of hospital admissions resulting from motor vehicle crashes. The data compares Fridays on the 6th of a month with Fridays on the 13th of the same month. The purpose is to determine if there is a significant difference in admissions when the 13th falls on a Friday, which some believe may be an "unlucky" day.
### Presented Data:
The table below shows the number of admissions for each date:
- **Friday the 6th:**
- 12, 5, 10, 8, 9
- **Friday the 13th:**
- 10, 14, 10, 14, 13
### Analysis:
The statistical measure we are using is the 95% confidence interval to estimate the mean of the population differences in admissions between these two dates. Each "difference" (d) is calculated as the admission number on Friday the 6th minus the admission number on Friday the 13th.
\[ \text{Mean difference (\( \mu_d \))} < \text{Mean of differences calculated} < \mu_d \]
**Note:** The exact bounds of the confidence interval should be calculated and rounded to two decimal places.
### Interpretation:
Based on this confidence interval, we need to evaluate whether we can reject the claim that hospital admissions are unaffected on Friday the 13th.
**Options:**
- **A.** Yes, because the confidence interval includes zero.
- **B.** No, since it includes zero, indicating no significant difference.
- **C.** No, because the interval does not include zero.
- **D.** Yes, because it does not include zero, indicating a significant difference.
The correct option will depend on the calculated confidence interval bounds.
This example illustrates how statistical tools, like confidence intervals, help in determining the likelihood of observed effects and guiding decision-making based on data analysis.
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