Hospital emergency rooms (ERs) have a bad reputation for long wait times. To improve their image, many hospitals have worked hard to reduce their ER wait times and frequently advertise their improved, low ER wait times. Lawnwood Regional Medical Center recently advertised a 20 minute or less wait time at their ER. An accreditation agency is suspicious of this low advertised wait time and would like to test the hospital's claim. A random sample of 96 ER visits to Lawnwood Regional Medical Center was examined and the mean wait time of the sample was found to be 21.15 minutes. Using a significance level of 0.5%, can the accreditation agency conclude that the hospital's claim about ER wait times is false? Assume that the standard deviation of the wait times of all ER visits at Lawnwood Regional Medical Center is known to be 3.63 minutes. Use the critical value method. State the null and alternative hypothesis for this test. Ho:? v H₁: ? ✓ Determine if this test is left-tailed, right-tailed, or two-tailed. Oright-tailed Otwo-tailed O left-tailed Should the standard normal (2) distribution or Student's (t) distribution be used for this test? O The standard normal (2) distribution should be used The Student's t distribution should be used Determine the critical value(s) for this hypothesis test. Round the solution (s) to two decimal places. If more than one critical value exists, enter the solutions using a comma-separated list. Determine the test statistic. Round the solution to two decimal places.
Hospital emergency rooms (ERs) have a bad reputation for long wait times. To improve their image, many hospitals have worked hard to reduce their ER wait times and frequently advertise their improved, low ER wait times. Lawnwood Regional Medical Center recently advertised a 20 minute or less wait time at their ER. An accreditation agency is suspicious of this low advertised wait time and would like to test the hospital's claim. A random sample of 96 ER visits to Lawnwood Regional Medical Center was examined and the mean wait time of the sample was found to be 21.15 minutes. Using a significance level of 0.5%, can the accreditation agency conclude that the hospital's claim about ER wait times is false? Assume that the standard deviation of the wait times of all ER visits at Lawnwood Regional Medical Center is known to be 3.63 minutes. Use the critical value method. State the null and alternative hypothesis for this test. Ho:? v H₁: ? ✓ Determine if this test is left-tailed, right-tailed, or two-tailed. Oright-tailed Otwo-tailed O left-tailed Should the standard normal (2) distribution or Student's (t) distribution be used for this test? O The standard normal (2) distribution should be used The Student's t distribution should be used Determine the critical value(s) for this hypothesis test. Round the solution (s) to two decimal places. If more than one critical value exists, enter the solutions using a comma-separated list. Determine the test statistic. Round the solution to two decimal places.
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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#28). Please show how to solve critical value and test statistic
![### Hypothesis Testing for ER Wait Times at Lawnwood Regional Medical Center
Hospital emergency rooms (ERs) frequently receive criticism for long wait times. To enhance their reputation, many hospitals have strived to reduce ER wait times and often advertise their improved wait times.
Lawnwood Regional Medical Center has recently promoted a wait time of 20 minutes or less at their ER. However, an accreditation agency is skeptical of this advertised wait time and seeks to verify the hospital’s claim through statistical analysis.
A random sample of 96 ER visits to Lawnwood Regional Medical Center revealed a mean wait time of 21.15 minutes.
**Objective:** Using a significance level of 0.5%, can the accreditation agency conclude that the hospital's claim about ER wait times is false? Assume that the standard deviation of wait times for all ER visits at Lawnwood Regional Medical Center is 3.63 minutes. The critical value method will be employed.
#### Null and Alternative Hypothesis
State the null and alternative hypothesis for this test:
- **H₀**: (The null hypothesis, usually states there is no effect or no difference.)
- **H₁**: (The alternative hypothesis, usually represents what we are trying to find evidence for.)
#### Tail Determination
Determine if this test is left-tailed, right-tailed, or two-tailed:
- \[ \] right-tailed
- \[ \] two-tailed
- \[ \] left-tailed
#### Distribution Selection
Which distribution should be used for this test, standard normal (z) distribution or Student's (t) distribution?
- \[ \] The standard normal (z) distribution should be used
- \[ \] The Student’s (t) distribution should be used
#### Critical Value(s)
Determine the critical value(s) for this hypothesis test. Round the solution to two decimal places. If more than one critical value exists, enter the solutions using a comma-separated list.
#### Test Statistic Calculation
Determine the test statistic. Round the solution to two decimal places.
These steps outline the process of hypothesis testing to verify the accuracy of Lawnwood Regional Medical Center's advertised ER wait times. Accurate analysis and interpretation of data are paramount in making informed decisions that affect hospital operations and patient satisfaction.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F090c748e-ae6e-4835-a77f-8d1d8bf06681%2Fd5e9f246-de45-4d20-8067-6604b24c3b53%2Fmtkj72n_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Hypothesis Testing for ER Wait Times at Lawnwood Regional Medical Center
Hospital emergency rooms (ERs) frequently receive criticism for long wait times. To enhance their reputation, many hospitals have strived to reduce ER wait times and often advertise their improved wait times.
Lawnwood Regional Medical Center has recently promoted a wait time of 20 minutes or less at their ER. However, an accreditation agency is skeptical of this advertised wait time and seeks to verify the hospital’s claim through statistical analysis.
A random sample of 96 ER visits to Lawnwood Regional Medical Center revealed a mean wait time of 21.15 minutes.
**Objective:** Using a significance level of 0.5%, can the accreditation agency conclude that the hospital's claim about ER wait times is false? Assume that the standard deviation of wait times for all ER visits at Lawnwood Regional Medical Center is 3.63 minutes. The critical value method will be employed.
#### Null and Alternative Hypothesis
State the null and alternative hypothesis for this test:
- **H₀**: (The null hypothesis, usually states there is no effect or no difference.)
- **H₁**: (The alternative hypothesis, usually represents what we are trying to find evidence for.)
#### Tail Determination
Determine if this test is left-tailed, right-tailed, or two-tailed:
- \[ \] right-tailed
- \[ \] two-tailed
- \[ \] left-tailed
#### Distribution Selection
Which distribution should be used for this test, standard normal (z) distribution or Student's (t) distribution?
- \[ \] The standard normal (z) distribution should be used
- \[ \] The Student’s (t) distribution should be used
#### Critical Value(s)
Determine the critical value(s) for this hypothesis test. Round the solution to two decimal places. If more than one critical value exists, enter the solutions using a comma-separated list.
#### Test Statistic Calculation
Determine the test statistic. Round the solution to two decimal places.
These steps outline the process of hypothesis testing to verify the accuracy of Lawnwood Regional Medical Center's advertised ER wait times. Accurate analysis and interpretation of data are paramount in making informed decisions that affect hospital operations and patient satisfaction.
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