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 the a = 0.10 level of significance? a. For this study, we should use t-test for a population mean b. The null and alternative hypotheses would be: Ho: μ = + 93 H₁: u+ + 93 c. The test statistic t = 1.181 ✓(please show your answer to 3 decimal places.) d. The p-value = (Please show your answer to 4 decimal places.) e. The p-value is s a f. Based on this, we should Select an answer the null hypothesis. g. Thus, the final conclusion is that ... The data suggest the populaton mean is significantly more than 93 at a = 0.10, so there is statistically significant evidence to conclude that the population mean amount of alcohol consumed by college students is more than 93 liters per year. The data suggest the population mean is not significantly more than 93 at a = 0.10, so there is statistically insignificant evidence to conclude that the population mean amount of alcohol consumed by college students is equal to 93 liters per year. The data suggest that the population mean amount of alcohol consumed by college students is not significantly more than 93 liters per year at a = 0.10, so there is statistically insignificant evidence to conclude that the population mean amount of alcohol consumed by college students is more than 93 liters per year.
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 the a = 0.10 level of significance? a. For this study, we should use t-test for a population mean b. The null and alternative hypotheses would be: Ho: μ = + 93 H₁: u+ + 93 c. The test statistic t = 1.181 ✓(please show your answer to 3 decimal places.) d. The p-value = (Please show your answer to 4 decimal places.) e. The p-value is s a f. Based on this, we should Select an answer the null hypothesis. g. Thus, the final conclusion is that ... The data suggest the populaton mean is significantly more than 93 at a = 0.10, so there is statistically significant evidence to conclude that the population mean amount of alcohol consumed by college students is more than 93 liters per year. The data suggest the population mean is not significantly more than 93 at a = 0.10, so there is statistically insignificant evidence to conclude that the population mean amount of alcohol consumed by college students is equal to 93 liters per year. The data suggest that the population mean amount of alcohol consumed by college students is not significantly more than 93 liters per year at a = 0.10, so there is statistically insignificant evidence to conclude that the population mean amount of alcohol consumed by college students is more than 93 liters per year.
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.4: Distributions Of Data
Problem 7PPS
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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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd1a73d04-4829-40e4-8e78-0a30aa84e71e%2F82370140-4c82-4d91-ae9b-cdd25379ae1c%2Fqhpeqxa_processed.png&w=3840&q=75)
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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