You may need to use the appropriate technology to answer this question. Guitars R.US has three stores located in three different areas. Random samples of the sales of the three stores (in $1,000) are shown below. Please note the sample sizes are not equal. Store 1 87 77 78 91 82 Store 2 87 88 O Ho: store 1 H: Hstore 1 83 86 (a) Compute the overall mean. 84.25 HStore 2 Store 3 Store 2 79 (b) State the null and alternative hypotheses to test for difference in the population mean sales among the three stores. O Ho: Store 1 #Store 2 * Store 3 H: At least two of the store means are different. 84 89 Store 3 store 3 Ho: Store 1 Store 2 = Store 3 H: At least two of the store means are different. 10 Hei Hor=#store 2 #store 3
You may need to use the appropriate technology to answer this question. Guitars R.US has three stores located in three different areas. Random samples of the sales of the three stores (in $1,000) are shown below. Please note the sample sizes are not equal. Store 1 87 77 78 91 82 Store 2 87 88 O Ho: store 1 H: Hstore 1 83 86 (a) Compute the overall mean. 84.25 HStore 2 Store 3 Store 2 79 (b) State the null and alternative hypotheses to test for difference in the population mean sales among the three stores. O Ho: Store 1 #Store 2 * Store 3 H: At least two of the store means are different. 84 89 Store 3 store 3 Ho: Store 1 Store 2 = Store 3 H: At least two of the store means are different. 10 Hei Hor=#store 2 #store 3
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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![## Sales Analysis of Guitars R Us Stores
**Summary:**
Guitars R Us has three stores located in different areas. Random samples of the sales (in $1,000) from these stores are presented in the table. Note that sample sizes are unequal.
### Sales Data:
| | Store 1 | Store 2 | Store 3 |
|---------|---------|---------|---------|
| Sales 1 | 87 | 87 | 79 |
| Sales 2 | 77 | 88 | 84 |
| Sales 3 | 78 | 83 | 89 |
| Sales 4 | 91 | 86 | |
| Sales 5 | 82 | | |
### (a) Compute the Overall Mean:
The overall mean of the sales is computed to be **84.25**.
### (b) Hypothesis Testing:
To test for differences in population mean sales among the three stores, the null and alternative hypotheses are stated as follows:
- Null Hypothesis, \( H_0 \): Store 1 = Store 2 = Store 3
- Alternative Hypothesis, \( H_a \): At least two of the store means are different.
The correct option for the alternative hypothesis selected is:
\[ H_a: \text{At least two of the store means are different.} \]
### (c) ANOVA Test:
The problem instructs to show the complete ANOVA table including the test statistic. The table should include columns for Source of Variation, Sum of Squares, Degrees of Freedom, Mean Square, and the F statistic.
The image of the laptop is unrelated to the content above.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7c919535-17ac-40c0-a926-0dbdaa63953a%2F4bb0a717-fe37-4c40-9972-334f998877c3%2Fztzjb99_processed.jpeg&w=3840&q=75)
Transcribed Image Text:## Sales Analysis of Guitars R Us Stores
**Summary:**
Guitars R Us has three stores located in different areas. Random samples of the sales (in $1,000) from these stores are presented in the table. Note that sample sizes are unequal.
### Sales Data:
| | Store 1 | Store 2 | Store 3 |
|---------|---------|---------|---------|
| Sales 1 | 87 | 87 | 79 |
| Sales 2 | 77 | 88 | 84 |
| Sales 3 | 78 | 83 | 89 |
| Sales 4 | 91 | 86 | |
| Sales 5 | 82 | | |
### (a) Compute the Overall Mean:
The overall mean of the sales is computed to be **84.25**.
### (b) Hypothesis Testing:
To test for differences in population mean sales among the three stores, the null and alternative hypotheses are stated as follows:
- Null Hypothesis, \( H_0 \): Store 1 = Store 2 = Store 3
- Alternative Hypothesis, \( H_a \): At least two of the store means are different.
The correct option for the alternative hypothesis selected is:
\[ H_a: \text{At least two of the store means are different.} \]
### (c) ANOVA Test:
The problem instructs to show the complete ANOVA table including the test statistic. The table should include columns for Source of Variation, Sum of Squares, Degrees of Freedom, Mean Square, and the F statistic.
The image of the laptop is unrelated to the content above.
![### ANOVA Test Analysis
**ANOVA Table Completion and Testing:**
a. **Hypotheses:**
- Null Hypothesis (\[H_0\]): \( \mu_1 = \mu_2 = \mu_3 \) (All means are equal)
- Alternative Hypothesis (\[H_a\]): At least two means are different.
b. **ANOVA Table Setup:**
| Source of Variation | Sum of Squares | Degrees of Freedom | Mean Square | F |
|---------------------|----------------|--------------------|-------------|-----|
| Between Treatments | | | | |
| Total | | | | |
- Fill in the table with the correct calculations for sum of squares, degrees of freedom, mean square, and F-statistic.
c. **P-Value and Test Conclusion:**
- P-Value: \( \text{p-value} \) = 0.004 (example value).
d. **Conclusion:**
- Based on the P-value:
- If \( \text{p-value} \leq 0.05 \), reject \( H_0 \) (there is significant evidence to suggest a difference among means).
- If \( \text{p-value} > 0.05 \), do not reject \( H_0 \).
### Instructions:
1. **Calculate ANOVA Components:**
- Use the formulas to calculate sum of squares for treatments and total, and determine mean square values.
- Calculate the F-statistic.
2. **Determine the Critical Values:**
- Compare critical F-value at a significance level of 0.05.
3. **Interpret Results:**
- Analyze results to conclude if there's significant difference among groups.
### Notes:
- Ensure calculations are rounded to four decimal places where applicable.
- Interpret data to understand implications of hypothesis testing in practical contexts.
Let's now proceed with detailed calculations and analysis in applying these principles.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7c919535-17ac-40c0-a926-0dbdaa63953a%2F4bb0a717-fe37-4c40-9972-334f998877c3%2Fhyeordq_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### ANOVA Test Analysis
**ANOVA Table Completion and Testing:**
a. **Hypotheses:**
- Null Hypothesis (\[H_0\]): \( \mu_1 = \mu_2 = \mu_3 \) (All means are equal)
- Alternative Hypothesis (\[H_a\]): At least two means are different.
b. **ANOVA Table Setup:**
| Source of Variation | Sum of Squares | Degrees of Freedom | Mean Square | F |
|---------------------|----------------|--------------------|-------------|-----|
| Between Treatments | | | | |
| Total | | | | |
- Fill in the table with the correct calculations for sum of squares, degrees of freedom, mean square, and F-statistic.
c. **P-Value and Test Conclusion:**
- P-Value: \( \text{p-value} \) = 0.004 (example value).
d. **Conclusion:**
- Based on the P-value:
- If \( \text{p-value} \leq 0.05 \), reject \( H_0 \) (there is significant evidence to suggest a difference among means).
- If \( \text{p-value} > 0.05 \), do not reject \( H_0 \).
### Instructions:
1. **Calculate ANOVA Components:**
- Use the formulas to calculate sum of squares for treatments and total, and determine mean square values.
- Calculate the F-statistic.
2. **Determine the Critical Values:**
- Compare critical F-value at a significance level of 0.05.
3. **Interpret Results:**
- Analyze results to conclude if there's significant difference among groups.
### Notes:
- Ensure calculations are rounded to four decimal places where applicable.
- Interpret data to understand implications of hypothesis testing in practical contexts.
Let's now proceed with detailed calculations and analysis in applying these principles.
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