Recovering from surgery: A new postsurgical treatment was compared with a standard treatment. Seven subjects received the new treatment, while seven others (the controls) received the standard treatment. The recovery times, in days, are given below. Treatment: 12 13 15 19 20 21 24 35 Control: 18 23 24 30 32 39 Send data to Excel Can you conclude that the mean recovery time for those receiving the new treatment is less than the mean for those receiving the standard treatment? Let μ₁ denote the mean recovery time for the new treatment. Use the a= 0.05 level of significance and the TI-84 Plus calculator. Part: 0/4 Part 1 of 4 A State the null and alternate hypotheses. Ho: < > 0=0 H₁: □□ Hi

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
icon
Related questions
Question
100%
### Recovering from Surgery: Comparing New and Standard Treatments

#### Study Overview:
A new postsurgical treatment was compared with a standard treatment. Seven subjects received the new treatment, while seven others (the controls) received the standard treatment. 

The recovery times, in days, for each group are presented below.

#### Recovery Times in Days:
**Treatment Group:**
- 12, 13, 15, 19, 20, 21, 24

**Control Group:**
- 18, 23, 24, 30, 32, 35, 39

#### Data Transfer Option:
- [Button labeled "Send data to Excel"]

#### Hypothesis Testing:
**Objective:**
Can you conclude that the mean recovery time for those receiving the new treatment is less than the mean for those receiving the standard treatment? 

Let \(\mu_1\) denote the mean recovery time for the new treatment.

Use the \(\alpha = 0.05\) level of significance and the TI-84 Plus calculator.

---

### Part 1 of 4:
**State the null and alternate hypotheses:**

- **Null Hypothesis (\(H_0\)):**
  - \(\mu_1 \geq \mu_2\)
  
- **Alternative Hypothesis (\(H_1\)):**
  - \(\mu_1 < \mu_2\)

### Graphs and Diagrams:
This section does not contain any graphs or diagrams. 

---

### Instructions for Students:

1. **Understand the Hypotheses:**
   - The null hypothesis (\(H_0\)) states there is no decrease in the mean recovery time for the new treatment compared to the standard treatment.
   - The alternative hypothesis (\(H_1\)) posits that the mean recovery time is indeed less for the new treatment.

2. **Use Statistical Tools:**
   - To test these hypotheses, you would typically calculate the sample means and variances of the two groups and perform a t-test for the difference in means.
   - Make sure to use the given level of significance (\(\alpha = 0.05\)) in your calculations to determine if the results are statistically significant.

3. **Interpreting Results:**
   - If you reject the null hypothesis, it would suggest that the new treatment reduces recovery time compared to the standard treatment.
   - If you fail to reject the null hypothesis,
Transcribed Image Text:### Recovering from Surgery: Comparing New and Standard Treatments #### Study Overview: A new postsurgical treatment was compared with a standard treatment. Seven subjects received the new treatment, while seven others (the controls) received the standard treatment. The recovery times, in days, for each group are presented below. #### Recovery Times in Days: **Treatment Group:** - 12, 13, 15, 19, 20, 21, 24 **Control Group:** - 18, 23, 24, 30, 32, 35, 39 #### Data Transfer Option: - [Button labeled "Send data to Excel"] #### Hypothesis Testing: **Objective:** Can you conclude that the mean recovery time for those receiving the new treatment is less than the mean for those receiving the standard treatment? Let \(\mu_1\) denote the mean recovery time for the new treatment. Use the \(\alpha = 0.05\) level of significance and the TI-84 Plus calculator. --- ### Part 1 of 4: **State the null and alternate hypotheses:** - **Null Hypothesis (\(H_0\)):** - \(\mu_1 \geq \mu_2\) - **Alternative Hypothesis (\(H_1\)):** - \(\mu_1 < \mu_2\) ### Graphs and Diagrams: This section does not contain any graphs or diagrams. --- ### Instructions for Students: 1. **Understand the Hypotheses:** - The null hypothesis (\(H_0\)) states there is no decrease in the mean recovery time for the new treatment compared to the standard treatment. - The alternative hypothesis (\(H_1\)) posits that the mean recovery time is indeed less for the new treatment. 2. **Use Statistical Tools:** - To test these hypotheses, you would typically calculate the sample means and variances of the two groups and perform a t-test for the difference in means. - Make sure to use the given level of significance (\(\alpha = 0.05\)) in your calculations to determine if the results are statistically significant. 3. **Interpreting Results:** - If you reject the null hypothesis, it would suggest that the new treatment reduces recovery time compared to the standard treatment. - If you fail to reject the null hypothesis,
Expert Solution
steps

Step by step

Solved in 2 steps with 2 images

Blurred answer
Similar questions
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman