MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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## Hypothesis Testing for Alcohol Consumption Among College Students

### Problem Statement
The average American consumes 93 liters of alcohol per year. Does the average college student consume more alcohol per year? A researcher surveyed 12 randomly selected college students and found that they averaged 100.5 liters of alcohol consumed per year with a standard deviation of 22 liters. What can be concluded at the \( \alpha = 0.10 \) level of significance?

### Steps to Solve

**a. Appropriate Test**  
For this study, we should use:
- **t-test for a population mean** ✔️

**b. Null and Alternative Hypotheses**

The null and alternative hypotheses would be:
- **Null Hypothesis (\( H_0 \))**:
  \[
  \mu = 93 \, \text{liters}
  \] ✔️
- **Alternative Hypothesis (\( H_1 \))**:
  \[
  \mu > 93 \, \text{liters}
  \] ✔️

**c. Calculate the Test Statistic**

The test statistic \( t \) can be calculated using the provided data:
- The sample mean \( \bar{x} = 100.5 \)
- The population mean \( \mu = 93 \)
- The sample standard deviation \( s = 22 \)
- The sample size \( n = 12 \)

\[
t = 1.181 \, (\text{rounded to 3 decimal places}) \] ✔️

**d. Determine the p-value**

The p-value is calculated based on the test statistic and degrees of freedom. 

\[
\text{p-value} = 0.1301 \, \,  (\text{rounded to 4 decimal places})
\]

**e. Compare the p-value to the Significance Level \( \alpha \)**

\[
\text{The p-value is} > \alpha
\]

**f. Decision**

Based on this, we should:
- **Fail to reject** the null hypothesis.

**g. Final Conclusion**

\[
\text{The final conclusion is that} \, \ldots
\]

### Conclusion Options
- \( \circ \) **The data suggest the population mean is significantly more than 93 at \( \alpha = 0.10 \), so there is statistically significant evidence to conclude that the population mean amount of alcohol consumed
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Transcribed Image Text:## Hypothesis Testing for Alcohol Consumption Among College Students ### Problem Statement The average American consumes 93 liters of alcohol per year. Does the average college student consume more alcohol per year? A researcher surveyed 12 randomly selected college students and found that they averaged 100.5 liters of alcohol consumed per year with a standard deviation of 22 liters. What can be concluded at the \( \alpha = 0.10 \) level of significance? ### Steps to Solve **a. Appropriate Test** For this study, we should use: - **t-test for a population mean** ✔️ **b. Null and Alternative Hypotheses** The null and alternative hypotheses would be: - **Null Hypothesis (\( H_0 \))**: \[ \mu = 93 \, \text{liters} \] ✔️ - **Alternative Hypothesis (\( H_1 \))**: \[ \mu > 93 \, \text{liters} \] ✔️ **c. Calculate the Test Statistic** The test statistic \( t \) can be calculated using the provided data: - The sample mean \( \bar{x} = 100.5 \) - The population mean \( \mu = 93 \) - The sample standard deviation \( s = 22 \) - The sample size \( n = 12 \) \[ t = 1.181 \, (\text{rounded to 3 decimal places}) \] ✔️ **d. Determine the p-value** The p-value is calculated based on the test statistic and degrees of freedom. \[ \text{p-value} = 0.1301 \, \, (\text{rounded to 4 decimal places}) \] **e. Compare the p-value to the Significance Level \( \alpha \)** \[ \text{The p-value is} > \alpha \] **f. Decision** Based on this, we should: - **Fail to reject** the null hypothesis. **g. Final Conclusion** \[ \text{The final conclusion is that} \, \ldots \] ### Conclusion Options - \( \circ \) **The data suggest the population mean is significantly more than 93 at \( \alpha = 0.10 \), so there is statistically significant evidence to conclude that the population mean amount of alcohol consumed
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