### Survey on Ankle Consultation PreferencesA previous survey asked people whom they would consult for an ankle issue. The following results were obtained:- **40%** said they would consult their **doctor**- **38%** said they would consult a **physical therapist (PT)**- **12%** said they would consult a **chiropractor**- **10%** said they would simply **rest at home** and stay off it for a few daysYou think that this model is no longer valid, so you decide to conduct a survey and find out for yourself. Relying on knowledge you gained in CMP 114, your favorite class of all time, you test the results to see if your hunch was right. Your survey produced the following results:| **Category** | **Count** ||------------------|-----------|| Doctor | 94 || PT | 80 || Chiropractor | 16 || Stay At Home | 10 |### Statistical AnalysisAnswer the following using a significance level of $ \alpha = 0.05 $:- **Chi-Squared** = [Choose]- **p-value** = [Choose]- **Decision** = [Choose]#### Question- Is the model still valid?

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Description: ### Survey on Ankle Consultation PreferencesA previous survey asked people whom they would consult for an ankle issue. The following results were obtained:- **40%** said they would consult their **doctor**- **38%** said they would consult a **physic

Answered: Answer the following. Use alpha = 0.05.…

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### Survey on Ankle Consultation Preferences

A previous survey asked people whom they would consult for an ankle issue. The following results were obtained:

- **40%** said they would consult their **doctor**
- **38%** said they would consult a **physical therapist (PT)**
- **12%** said they would consult a **chiropractor**
- **10%** said they would simply **rest at home** and stay off it for a few days

You think that this model is no longer valid, so you decide to conduct a survey and find out for yourself. Relying on knowledge you gained in CMP 114, your favorite class of all time, you test the results to see if your hunch was right. Your survey produced the following results:

| **Category** | **Count** |
|------------------|-----------|
| Doctor | 94 |
| PT | 80 |
| Chiropractor | 16 |
| Stay At Home | 10 |

### Statistical Analysis

Answer the following using a significance level of $ \alpha = 0.05 $:

- **Chi-Squared** = [Choose]
- **p-value** = [Choose]
- **Decision** = [Choose]

#### Question
- Is the model still valid?

Expert Solution

Step 1

The hypothesis is,

Null hypothesis:

$H_{0} :$ The model is valid.

Alternative hypothesis:

$H_{a} :$ The model is no longer valid.

The expected count is,

Category	Count	Proportion	Expected count
Doctor	94	0.40	$200 \times 0.40 = 80$
PT	80	0.38	$200 \times 0.38 = 76$
Chiropractor	16	0.12	$200 \times 0.12 = 24$
Stay At Home	10	0.10	$200 \times 0.10 = 20$
Total	200

The chi-squared test statistic value is,

$\begin{array}{rcl} χ^{2} & = & Sum of [\frac{{(Observed - Expected)}^{2}}{Expected}] \\ = & \frac{{(94 - 80)}^{2}}{80} + \frac{{(80 - 76)}^{2}}{76} + \frac{{(16 - 24)}^{2}}{24} + \frac{{(10 - 20)}^{2}}{20} \\ = & 2.4500 + 0.2105 + 2.6667 + 5.0000 \\ = & 10.3272 \end{array}$

Thus, the chi-squared test statistic value is 10.3272.

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