Determine the appropriate conclusion for this hypothesis test. O The sample data provide sufficient evidence to reject the alternative hypothesis that the patient has sustained high cholesterol and thus we conclude that the patient's cholesterol level is likely at or below 225 mg/dL. O The sample data do not provide sufficient evidence to reject the alternative hypothesis that the patient has sustained high cholesterol and thus we conclude that the patient's cholesterol level is likely above 225 mg/dL. O The sample data provide sufficient evidence to reject the null hypothesis that the mean cholesterol level of the patient is not more than 225 mg/dL and thus we conclude that it is likely the patient has sustained high cholesterol. O The sample data do not provide sufficient evidence to reject the null hypothesis that the mean cholesterol level of the patient is not more than 225 mg/dL and thus we conclude that it is likely the patient does not currently have sustained high cholesterol.
Determine the appropriate conclusion for this hypothesis test. O The sample data provide sufficient evidence to reject the alternative hypothesis that the patient has sustained high cholesterol and thus we conclude that the patient's cholesterol level is likely at or below 225 mg/dL. O The sample data do not provide sufficient evidence to reject the alternative hypothesis that the patient has sustained high cholesterol and thus we conclude that the patient's cholesterol level is likely above 225 mg/dL. O The sample data provide sufficient evidence to reject the null hypothesis that the mean cholesterol level of the patient is not more than 225 mg/dL and thus we conclude that it is likely the patient has sustained high cholesterol. O The sample data do not provide sufficient evidence to reject the null hypothesis that the mean cholesterol level of the patient is not more than 225 mg/dL and thus we conclude that it is likely the patient does not currently have sustained high cholesterol.
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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![### High Cholesterol Risk Assessment
High cholesterol is one of the major risk factors for heart disease. A total cholesterol reading above 225 mg/dL is considered high.
#### Case Study:
A physician is concerned that a patient may be at risk for high cholesterol. To accurately measure the patient's average cholesterol level, the physician instructs the patient to come into the office once a week for 8 weeks for a blood lipid screening. The results of these 8 measurements are listed below:
**Cholesterol Measurements (in mg/dL):**
226, 233, 236, 229, 230, 221, 233, 233
#### Hypothesis Testing:
To test the hypothesis that the patient's cholesterol level is greater than 225 mg/dL, we use the critical value method with a significance level of 1%. Assume that the distribution of all cholesterol measurements from this patient is approximately normally distributed.
**Steps for Hypothesis Testing:**
1. **State the Null and Alternative Hypotheses:**
\[
H_0 : \mu \leq 225 \quad \text{(Null Hypothesis: The patient's average cholesterol level is less than or equal to 225 mg/dL)}
\]
\[
H_1 : \mu > 225 \quad \text{(Alternative Hypothesis: The patient's average cholesterol level is greater than 225 mg/dL)}
\]
2. **Determine the Type of Test:**
- **Right-tailed test**
- **Two-tailed test**
- **Left-tailed test**
In this case, since we are testing if the cholesterol level is greater than 225 mg/dL, it is a **right-tailed test**.
#### Analysis:
To proceed with the analysis, compute the sample mean and standard deviation of the 8 measurements. Then, use the t-distribution and the significance level (1%) to find the critical value. Compare the test statistic to the critical value to determine whether to reject the null hypothesis.
This structured approach helps in evaluating whether the patient’s cholesterol levels are significantly higher than 225 mg/dL, aiding in further clinical decision-making.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Faf14cf2c-4c6b-44b0-8c19-b82da3615fd0%2F10a990a1-e725-41bb-8e8a-138e0cb1b7e3%2Ftcnze1v_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### High Cholesterol Risk Assessment
High cholesterol is one of the major risk factors for heart disease. A total cholesterol reading above 225 mg/dL is considered high.
#### Case Study:
A physician is concerned that a patient may be at risk for high cholesterol. To accurately measure the patient's average cholesterol level, the physician instructs the patient to come into the office once a week for 8 weeks for a blood lipid screening. The results of these 8 measurements are listed below:
**Cholesterol Measurements (in mg/dL):**
226, 233, 236, 229, 230, 221, 233, 233
#### Hypothesis Testing:
To test the hypothesis that the patient's cholesterol level is greater than 225 mg/dL, we use the critical value method with a significance level of 1%. Assume that the distribution of all cholesterol measurements from this patient is approximately normally distributed.
**Steps for Hypothesis Testing:**
1. **State the Null and Alternative Hypotheses:**
\[
H_0 : \mu \leq 225 \quad \text{(Null Hypothesis: The patient's average cholesterol level is less than or equal to 225 mg/dL)}
\]
\[
H_1 : \mu > 225 \quad \text{(Alternative Hypothesis: The patient's average cholesterol level is greater than 225 mg/dL)}
\]
2. **Determine the Type of Test:**
- **Right-tailed test**
- **Two-tailed test**
- **Left-tailed test**
In this case, since we are testing if the cholesterol level is greater than 225 mg/dL, it is a **right-tailed test**.
#### Analysis:
To proceed with the analysis, compute the sample mean and standard deviation of the 8 measurements. Then, use the t-distribution and the significance level (1%) to find the critical value. Compare the test statistic to the critical value to determine whether to reject the null hypothesis.
This structured approach helps in evaluating whether the patient’s cholesterol levels are significantly higher than 225 mg/dL, aiding in further clinical decision-making.
![### Hypothesis Testing: Cholesterol Levels
#### Distribution Selection
- **The standard normal (z) distribution should be used**
- **The Student's t distribution should be used**
#### Determining Critical Values
- **Instruction:** Determine the critical value(s) for this hypothesis test. Round the solution(s) to four decimal places. If more than one critical value exists, enter the solutions using a comma-separated list.
```
[Enter critical values here]
```
#### Determining the Test Statistic
- **Instruction:** Determine the test statistic. Round the solution to four decimal places.
```
[Enter test statistic here]
```
#### Conclusion for Hypothesis Test
- **Instruction:** Determine the appropriate conclusion for this hypothesis test.
1. **The sample data provide sufficient evidence to reject the alternative hypothesis that the patient has sustained high cholesterol and thus we conclude that the patient's cholesterol level is likely at or below 225 mg/dL.**
2. **The sample data do not provide sufficient evidence to reject the alternative hypothesis that the patient has sustained high cholesterol and thus we conclude that the patient’s cholesterol level is likely above 225 mg/dL.**
3. **The sample data provide sufficient evidence to reject the null hypothesis that the mean cholesterol level of the patient is not more than 225 mg/dL and thus we conclude that it is likely the patient has sustained high cholesterol.**
4. **The sample data do not provide sufficient evidence to reject the null hypothesis that the mean cholesterol level of the patient is not more than 225 mg/dL and thus we conclude that it is likely the patient does not currently have sustained high cholesterol.**
---
#### Additional Information
- **Weather Information**: 76°F, Mostly clear
- **Note**: No graphs or diagrams were present in the provided text. The instructions and multiple-choice answers were provided for an educational setting related to hypothesis testing in statistics.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Faf14cf2c-4c6b-44b0-8c19-b82da3615fd0%2F10a990a1-e725-41bb-8e8a-138e0cb1b7e3%2Ffo7r5q_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Hypothesis Testing: Cholesterol Levels
#### Distribution Selection
- **The standard normal (z) distribution should be used**
- **The Student's t distribution should be used**
#### Determining Critical Values
- **Instruction:** Determine the critical value(s) for this hypothesis test. Round the solution(s) to four decimal places. If more than one critical value exists, enter the solutions using a comma-separated list.
```
[Enter critical values here]
```
#### Determining the Test Statistic
- **Instruction:** Determine the test statistic. Round the solution to four decimal places.
```
[Enter test statistic here]
```
#### Conclusion for Hypothesis Test
- **Instruction:** Determine the appropriate conclusion for this hypothesis test.
1. **The sample data provide sufficient evidence to reject the alternative hypothesis that the patient has sustained high cholesterol and thus we conclude that the patient's cholesterol level is likely at or below 225 mg/dL.**
2. **The sample data do not provide sufficient evidence to reject the alternative hypothesis that the patient has sustained high cholesterol and thus we conclude that the patient’s cholesterol level is likely above 225 mg/dL.**
3. **The sample data provide sufficient evidence to reject the null hypothesis that the mean cholesterol level of the patient is not more than 225 mg/dL and thus we conclude that it is likely the patient has sustained high cholesterol.**
4. **The sample data do not provide sufficient evidence to reject the null hypothesis that the mean cholesterol level of the patient is not more than 225 mg/dL and thus we conclude that it is likely the patient does not currently have sustained high cholesterol.**
---
#### Additional Information
- **Weather Information**: 76°F, Mostly clear
- **Note**: No graphs or diagrams were present in the provided text. The instructions and multiple-choice answers were provided for an educational setting related to hypothesis testing in statistics.
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