4. The Coca-Cola Company reported that the mean per capital annual sales of its beverages in the United States was 423 eight-ounce servings. Suppose you are curious whether the consump- tion of Coca-Cola beverages is higher in Atlanta, Georgia, the location of Coca-Colas corporate headquarters. A sample of 36 individuals from the Atlanta area showed a sample mean annual
4. The Coca-Cola Company reported that the mean per capital annual sales of its beverages in the United States was 423 eight-ounce servings. Suppose you are curious whether the consump- tion of Coca-Cola beverages is higher in Atlanta, Georgia, the location of Coca-Colas corporate headquarters. A sample of 36 individuals from the Atlanta area showed a sample mean annual
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Author:Amos Gilat
Publisher:Amos Gilat
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Problem 1P
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![### Coca-Cola Consumption Study
**Problem Statement:**
The Coca-Cola Company reported that the mean per capita annual sales of its beverages in the United States was 423 eight-ounce servings. Suppose you are curious whether the consumption of Coca-Cola beverages is higher in Atlanta, Georgia, the location of Coca-Cola's corporate headquarters. A sample of 36 individuals from the Atlanta area showed a sample mean annual consumption of 460.4 eight-ounce servings with a standard deviation of \( s = 101.9 \) ounces. Using \( \alpha = 0.05 \), do the sample results support the conclusion that mean annual consumption of Coca-Cola beverage products is higher in Atlanta?
**Tasks:**
**a. Formulate the hypotheses for this application.**
- **Null Hypothesis (\( H_0 \))**: The mean annual consumption of Coca-Cola beverages in Atlanta is equal to the mean national consumption.
\[
H_0: \mu = 423
\]
- **Alternative Hypothesis (\( H_a \))**: The mean annual consumption of Coca-Cola beverages in Atlanta is greater than the mean national consumption.
\[
H_a: \mu > 423
\]
**b. Compute the critical value.**
- For a one-tailed test at \( \alpha = 0.05 \) with \( n = 36 \):
- Degrees of freedom \( df = n - 1 = 35 \)
- Critical value can be found using the t-distribution table or a statistical calculator.
**Compute the P-value:**
- Calculate the test statistic using the formula:
\[
t = \frac{\bar{X} - \mu_0}{s / \sqrt{n}}
\]
Where:
\[
\bar{X} = 460.4, \quad \mu_0 = 423, \quad s = 101.9, \quad n = 36
\]
- Use the resulting test statistic to find the P-value from the t-distribution.
**c. What is your conclusion?**
- Compare the P-value with \( \alpha \):
- If \( \text{P-value} < \alpha \), reject the null hypothesis.
- If \( \text{P-value} \geq \alpha \), do not reject the null hypothesis.
- Based](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F53c8a81f-874c-4d59-9446-0d95f9a2a58d%2F8f937d99-8b3f-43a4-8858-1f4086147c57%2Fp6833tbw_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Coca-Cola Consumption Study
**Problem Statement:**
The Coca-Cola Company reported that the mean per capita annual sales of its beverages in the United States was 423 eight-ounce servings. Suppose you are curious whether the consumption of Coca-Cola beverages is higher in Atlanta, Georgia, the location of Coca-Cola's corporate headquarters. A sample of 36 individuals from the Atlanta area showed a sample mean annual consumption of 460.4 eight-ounce servings with a standard deviation of \( s = 101.9 \) ounces. Using \( \alpha = 0.05 \), do the sample results support the conclusion that mean annual consumption of Coca-Cola beverage products is higher in Atlanta?
**Tasks:**
**a. Formulate the hypotheses for this application.**
- **Null Hypothesis (\( H_0 \))**: The mean annual consumption of Coca-Cola beverages in Atlanta is equal to the mean national consumption.
\[
H_0: \mu = 423
\]
- **Alternative Hypothesis (\( H_a \))**: The mean annual consumption of Coca-Cola beverages in Atlanta is greater than the mean national consumption.
\[
H_a: \mu > 423
\]
**b. Compute the critical value.**
- For a one-tailed test at \( \alpha = 0.05 \) with \( n = 36 \):
- Degrees of freedom \( df = n - 1 = 35 \)
- Critical value can be found using the t-distribution table or a statistical calculator.
**Compute the P-value:**
- Calculate the test statistic using the formula:
\[
t = \frac{\bar{X} - \mu_0}{s / \sqrt{n}}
\]
Where:
\[
\bar{X} = 460.4, \quad \mu_0 = 423, \quad s = 101.9, \quad n = 36
\]
- Use the resulting test statistic to find the P-value from the t-distribution.
**c. What is your conclusion?**
- Compare the P-value with \( \alpha \):
- If \( \text{P-value} < \alpha \), reject the null hypothesis.
- If \( \text{P-value} \geq \alpha \), do not reject the null hypothesis.
- Based
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