Do the needs of patients in the emergency room differ for those who come by car vs. those by ambulance? Of the randomly selected emergency room patients who came by car 54 had an injury, 53 were sick, 37 had heart problems and 67 had other needs. Of the randomly selected emergency room patients who came by ambulance 45 had an injury, 22 were sick, 43 had heart problems and 30 had other needs. Conduct the appropriate hypothesis test using an a = 0.01 level of significance. a. What is the correct statistical test to use? O Homogeneity Goodness-of-Fit O Independence Paired t-test b. What are the null and alternative hypotheses? Ho: O Means of transportation to the emergency room and emergency room needs are independent. O The distribution of emergency room needs for patients who come by car is the same as it is for patients who come by ambulance. O The distribution of emergency room needs for patients who come by car is not the same as it is for patients who come by ambulance. O Means of transportation to the emergency room and emergency room needs are dependent.

Big Ideas Math A Bridge To Success Algebra 1: Student Edition 2015
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ISBN:9781680331141
Author:HOUGHTON MIFFLIN HARCOURT
Publisher:HOUGHTON MIFFLIN HARCOURT
Chapter4: Writing Linear Equations
Section: Chapter Questions
Problem 14CR
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**Analysis of Emergency Room Patient Needs Based on Transportation Method**

The study investigates whether the needs of patients in the emergency room differ depending on whether they arrive by car or ambulance. The data collected includes:

- Patients arriving by car: 
  - 54 had an injury
  - 53 were sick
  - 37 had heart problems
  - 67 had other needs

- Patients arriving by ambulance:
  - 45 had an injury
  - 22 were sick
  - 43 had heart problems
  - 30 had other needs

The hypothesis test will be conducted at a significance level of α = 0.01.

**Questions:**

a. **Correct Statistical Test to Use:**

   - Homogeneity
   - Goodness-of-Fit
   - Independence
   - Paired t-test

b. **Null and Alternative Hypotheses:**

   \( H_0: \)

   - Means of transportation to the emergency room and emergency room needs are independent.
   - The distribution of emergency room needs for patients who come by car is the same as it is for patients who come by ambulance.
   - The distribution of emergency room needs for patients who come by car is not the same as it is for patients who come by ambulance.
   - Means of transportation to the emergency room and emergency room needs are dependent.
Transcribed Image Text:**Analysis of Emergency Room Patient Needs Based on Transportation Method** The study investigates whether the needs of patients in the emergency room differ depending on whether they arrive by car or ambulance. The data collected includes: - Patients arriving by car: - 54 had an injury - 53 were sick - 37 had heart problems - 67 had other needs - Patients arriving by ambulance: - 45 had an injury - 22 were sick - 43 had heart problems - 30 had other needs The hypothesis test will be conducted at a significance level of α = 0.01. **Questions:** a. **Correct Statistical Test to Use:** - Homogeneity - Goodness-of-Fit - Independence - Paired t-test b. **Null and Alternative Hypotheses:** \( H_0: \) - Means of transportation to the emergency room and emergency room needs are independent. - The distribution of emergency room needs for patients who come by car is the same as it is for patients who come by ambulance. - The distribution of emergency room needs for patients who come by car is not the same as it is for patients who come by ambulance. - Means of transportation to the emergency room and emergency room needs are dependent.
**Hypothesis Testing for Emergency Room Needs Based on Transportation**

**H₁:**

- **Options for Hypothesis:**

  - The distribution of emergency room needs for patients who come by car is the same as it is for patients who come by ambulance.

  - Means of transportation to the emergency room and emergency room needs are independent.

  - Means of transportation to the emergency room and emergency room needs are dependent.

  - The distribution of emergency room needs for patients who come by car is not the same as it is for patients who come by ambulance.

**Steps for Hypothesis Testing:**

c. **Test Statistic:** 
   - Enter the calculated test statistic value to three decimal places.

d. **P-value for this Sample:**
   - Enter the p-value for the sample to four decimal places.

e. **Comparison with Alpha (α):**
   - Select an option to indicate whether the p-value is <, =, or > α.

f. **Decision on the Null Hypothesis:**
   - Choose whether to:
     - Accept the null
     - Reject the null
     - Fail to reject the null

g. **Final Conclusion:**
   - Based on the analysis, select the appropriate conclusion:
     - There is sufficient evidence to conclude that the distribution of emergency room needs for patients who come by car is the same as it is for patients who come by ambulance.
     - There is insufficient evidence to conclude that the distribution of emergency room needs for patients who come by car is not the same as it is for patients who come by ambulance.
     - There is insufficient evidence to conclude that the means of transportation to the emergency room and emergency room needs are dependent.
     - There is sufficient evidence to conclude that the means of transportation to the emergency room and emergency room needs are dependent.
     - There is sufficient evidence to conclude that the distribution of emergency room needs for patients who come by car is not the same as it is for patients who come by ambulance.
Transcribed Image Text:**Hypothesis Testing for Emergency Room Needs Based on Transportation** **H₁:** - **Options for Hypothesis:** - The distribution of emergency room needs for patients who come by car is the same as it is for patients who come by ambulance. - Means of transportation to the emergency room and emergency room needs are independent. - Means of transportation to the emergency room and emergency room needs are dependent. - The distribution of emergency room needs for patients who come by car is not the same as it is for patients who come by ambulance. **Steps for Hypothesis Testing:** c. **Test Statistic:** - Enter the calculated test statistic value to three decimal places. d. **P-value for this Sample:** - Enter the p-value for the sample to four decimal places. e. **Comparison with Alpha (α):** - Select an option to indicate whether the p-value is <, =, or > α. f. **Decision on the Null Hypothesis:** - Choose whether to: - Accept the null - Reject the null - Fail to reject the null g. **Final Conclusion:** - Based on the analysis, select the appropriate conclusion: - There is sufficient evidence to conclude that the distribution of emergency room needs for patients who come by car is the same as it is for patients who come by ambulance. - There is insufficient evidence to conclude that the distribution of emergency room needs for patients who come by car is not the same as it is for patients who come by ambulance. - There is insufficient evidence to conclude that the means of transportation to the emergency room and emergency room needs are dependent. - There is sufficient evidence to conclude that the means of transportation to the emergency room and emergency room needs are dependent. - There is sufficient evidence to conclude that the distribution of emergency room needs for patients who come by car is not the same as it is for patients who come by ambulance.
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