**Investigation of a New Bandage on Healing Times**A novel bandage has been developed to aid in the healing of small cuts. This innovative bandage features special air circulation holes and contains antiseptic within the bandage pad. In studies, controlled one-centimeter cuts in volunteers healed completely in an average of 11 days when utilizing the traditional bandage.**Objective:** Determine if the new bandage significantly reduces healing times. **Data:** Below are the healing times (in days) for similar cuts treated with the new bandage:- 9.5- 9.7- 10.5- 10.2- 10.8- 10.9- 10.1- 11.3- 9.9- 9.6- 11.2- 11.0- 10.0- 10.4- 11.4- 9.8**Analysis Methodology:**1. **Parametric Analysis:** Evaluate via statistical methods that assume a specific distribution.2. **Nonparametric Analysis:** Utilize both the sign test and the Wilcoxon signed-rank test to assess differences in healing times.The goal is to confirm any statistically significant reductions in healing times with the use of the new bandage.

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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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**Investigation of a New Bandage on Healing Times**

A novel bandage has been developed to aid in the healing of small cuts. This innovative bandage features special air circulation holes and contains antiseptic within the bandage pad. In studies, controlled one-centimeter cuts in volunteers healed completely in an average of 11 days when utilizing the traditional bandage.

**Objective:**
Determine if the new bandage significantly reduces healing times.

**Data:**
Below are the healing times (in days) for similar cuts treated with the new bandage:

- 9.5
- 9.7
- 10.5
- 10.2
- 10.8
- 10.9
- 10.1
- 11.3
- 9.9
- 9.6
- 11.2
- 11.0
- 10.0
- 10.4
- 11.4
- 9.8

**Analysis Methodology:**

1. **Parametric Analysis:** Evaluate via statistical methods that assume a specific distribution.
2. **Nonparametric Analysis:** Utilize both the sign test and the Wilcoxon signed-rank test to assess differences in healing times.

The goal is to confirm any statistically significant reductions in healing times with the use of the new bandage.

Expert Solution

Step 1

Data for healing time of new badges is 9.5, 9.7, 10.5, 10.2, 10.8, 10.9, 10.1, 11.3, 9.9, 9.6, 11.2, 11.0, 10.0, 10.4, 11.4, 9.8.

Hypotheses can be constructed as:

H₀: µ=11

H₁: µ<11

Step 2

Parametric test:

Test statistic can be obtained as:

$t = \frac{x - μ}{s / \sqrt{n}}$

Where,

$\begin{array}{rcl} x & = & \frac{9.5 + 9.7 + . . . + 9.8}{16} = 10.3938 \\ s & = & \sqrt{\frac{{(9.5 - 10.3938)}^{2} + {(9.7 - 10.3938)}^{2} + . . . + {(9.8 - 10.3938)}^{2}}{16 - 1}} = 0.6361 \end{array}$

Test statistic is:

$\begin{array}{rcl} t & = & \frac{10.3938 - 11}{0.6361 / \sqrt{16}} \\ = & - 3.8123 \end{array}$

Value of test statistic is -3.8123.

The test is one tailed.

The p value of the test statistic from the t-table is 0.0008.

The level of significance (α) = 0.05

Decision rule:

Reject H₀: if p value < level of significance (α)

Since, the p value is 0.0008 which is less than level of significance, therefore, the null hypothesis would be rejected and it can be concluded that there is sufficient evidence to conclude that new bandage significantly reduce healing time.

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