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
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
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.6: Applications And The Perron-frobenius Theorem
Problem 22EQ
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![### 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,](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff4d433bf-66f4-40c8-9ece-77f2345d877a%2F2329417f-d3f5-4547-87e3-8a4840b9493c%2Fah1owhp_processed.jpeg&w=3840&q=75)
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,
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