A study was carried out to compare mean customer satisfaction scores at service centers in city A, in city B, and in city C. The sample means on a scale of 0 to 10 were 8.4 in city A, 8.6 in city B, and 7.9 in city C. Each sample size = 100, MS error = 0.41, and the F test statistic = 27.4 has P-value <0.001. Complete parts a through d. a. What is the margin of error for separate 95% confidence intervals? (For df = 297, ¹.025 = 1.968.) margin of error = (Round to two decimal places as needed.)
A study was carried out to compare mean customer satisfaction scores at service centers in city A, in city B, and in city C. The sample means on a scale of 0 to 10 were 8.4 in city A, 8.6 in city B, and 7.9 in city C. Each sample size = 100, MS error = 0.41, and the F test statistic = 27.4 has P-value <0.001. Complete parts a through d. a. What is the margin of error for separate 95% confidence intervals? (For df = 297, ¹.025 = 1.968.) margin of error = (Round to two decimal places as needed.)
A First Course in Probability (10th Edition)
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![### Study Overview
A study was conducted to compare mean customer satisfaction scores at service centers in three cities: City A, City B, and City C. The scores were evaluated on a scale from 0 to 10, resulting in the following sample means:
- City A: 8.4
- City B: 8.6
- City C: 7.9
Each group had a sample size of 100. The mean square error (MS error) was reported at 0.41. An F test statistic of 27.4 was calculated, with a P-value of less than 0.001, indicating statistically significant differences between the groups.
### Margin of Error Calculation
#### Task
a. Calculate the margin of error for separate 95% confidence intervals. The degrees of freedom (df) is 297, and the critical t-value (\( t_{0.025} \)) is 1.968.
#### Formula
The margin of error (ME) is calculated using the following formula:
\[ \text{ME} = t \times \left(\frac{S}{\sqrt{n}}\right) \]
Where:
- \( t \) = critical t-value
- \( S \) = standard deviation of the sample
- \( n \) = sample size
### Instructions
1. Substitute the given values into the formula.
2. Round the final result to two decimal places as needed.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7617e6a3-d280-4f44-97ed-ed73937ef3e9%2Fe745f4b5-43b9-46eb-8f7b-14160b3fe5bc%2Fpli92t6_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Study Overview
A study was conducted to compare mean customer satisfaction scores at service centers in three cities: City A, City B, and City C. The scores were evaluated on a scale from 0 to 10, resulting in the following sample means:
- City A: 8.4
- City B: 8.6
- City C: 7.9
Each group had a sample size of 100. The mean square error (MS error) was reported at 0.41. An F test statistic of 27.4 was calculated, with a P-value of less than 0.001, indicating statistically significant differences between the groups.
### Margin of Error Calculation
#### Task
a. Calculate the margin of error for separate 95% confidence intervals. The degrees of freedom (df) is 297, and the critical t-value (\( t_{0.025} \)) is 1.968.
#### Formula
The margin of error (ME) is calculated using the following formula:
\[ \text{ME} = t \times \left(\frac{S}{\sqrt{n}}\right) \]
Where:
- \( t \) = critical t-value
- \( S \) = standard deviation of the sample
- \( n \) = sample size
### Instructions
1. Substitute the given values into the formula.
2. Round the final result to two decimal places as needed.
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