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 4 11 7 4 Friday the 13th 11 11 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 affected? O A. No, because the confidence interval does not include zero. O B. Yes, because the confidence interval does not include zero. O c. Yes, because the confidence interval includes zero. O D. No, because the confidence interval includes 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 4 11 7 4 Friday the 13th 11 11 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 affected? O A. No, because the confidence interval does not include zero. O B. Yes, because the confidence interval does not include zero. O c. Yes, because the confidence interval includes zero. O D. No, because the confidence interval includes 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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![### Data Analysis of Hospital Admissions on Friday the 13th
**Objective:**
To analyze whether the 13th day of a month falling on a Friday influences the number of hospital admissions due to motor vehicle crashes.
**Data Description:**
Hospital admission data on the 6th and 13th (when it falls on a Friday) of the same month:
- **Friday the 6th Admissions:** 4, 11, 7, 5, 4
- **Friday the 13th Admissions:** 11, 14, 13, 13, 14
**Analysis Task:**
Construct a 95% confidence interval for the mean of the differences between hospital admissions on these two Fridays. This tests the hypothesis that there is no significant change in hospital admissions.
**Definitions:**
- Each difference \( d \) is defined as: \( d = \) (Admissions on Friday the 6th) - (Admissions on Friday the 13th).
**Confidence Interval Calculation:**
- Define \( \mu_d \) as the mean value of all differences.
- Create a 95% confidence interval to assess \( \mu_d \).
**Confidence Interval:**
\[ \_\ < \mu_d < \_ \]
*(Values are to be calculated and rounded to two decimal places.)*
**Conclusion Assessment:**
Using the confidence interval, address the primary question:
- Can we reject the hypothesis that Fridays on the 13th lead to increased admissions?
**Answer Options:**
- **A.** No, because the confidence interval does not include zero.
- **B.** Yes, because the confidence interval does not include zero.
- **C.** Yes, because the confidence interval includes zero.
- **D.** No, because the confidence interval includes zero.
To complete the analysis, calculate the confidence interval and select the appropriate conclusion based on the results.
**Educational Note:**
Understanding confidence intervals is critical for assessing the significance of results in hypothesis testing. This helps determine if observed effects are due to random variations or indicate a real influence of the tested variable—in this case, the date.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2f0fb466-9e5e-42c4-aac7-4119dc8b6f62%2F15aefa96-afec-42e3-8468-6205de97f94a%2F5e00ifb_processed.png&w=3840&q=75)
Transcribed Image Text:### Data Analysis of Hospital Admissions on Friday the 13th
**Objective:**
To analyze whether the 13th day of a month falling on a Friday influences the number of hospital admissions due to motor vehicle crashes.
**Data Description:**
Hospital admission data on the 6th and 13th (when it falls on a Friday) of the same month:
- **Friday the 6th Admissions:** 4, 11, 7, 5, 4
- **Friday the 13th Admissions:** 11, 14, 13, 13, 14
**Analysis Task:**
Construct a 95% confidence interval for the mean of the differences between hospital admissions on these two Fridays. This tests the hypothesis that there is no significant change in hospital admissions.
**Definitions:**
- Each difference \( d \) is defined as: \( d = \) (Admissions on Friday the 6th) - (Admissions on Friday the 13th).
**Confidence Interval Calculation:**
- Define \( \mu_d \) as the mean value of all differences.
- Create a 95% confidence interval to assess \( \mu_d \).
**Confidence Interval:**
\[ \_\ < \mu_d < \_ \]
*(Values are to be calculated and rounded to two decimal places.)*
**Conclusion Assessment:**
Using the confidence interval, address the primary question:
- Can we reject the hypothesis that Fridays on the 13th lead to increased admissions?
**Answer Options:**
- **A.** No, because the confidence interval does not include zero.
- **B.** Yes, because the confidence interval does not include zero.
- **C.** Yes, because the confidence interval includes zero.
- **D.** No, because the confidence interval includes zero.
To complete the analysis, calculate the confidence interval and select the appropriate conclusion based on the results.
**Educational Note:**
Understanding confidence intervals is critical for assessing the significance of results in hypothesis testing. This helps determine if observed effects are due to random variations or indicate a real influence of the tested variable—in this case, the date.
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