Use the following for the next 3 problems. Is there a difference in the amount of airborne bacteria betw carpeted and uncarpeted rooms? In an experiment, 7 rooms were carpeted and 7 were left uncarpeted. The roc are similar in size and function. After a suitable period of time, the concentration of bacteria in the air measured (in units of bacteria per cubic foot) in all of these rooms. Assume the populations are norm- distributed. The following is a summary of the data: x S Carpeted rooms: 184 22.0 Uncarpeted rooms: 175 16.9 19. A 95% confidence interval for the difference in mean bacterial concentration in the air of carpeted ro versus uncarpeted rooms is (use 11 degrees of freedom).
Use the following for the next 3 problems. Is there a difference in the amount of airborne bacteria betw carpeted and uncarpeted rooms? In an experiment, 7 rooms were carpeted and 7 were left uncarpeted. The roc are similar in size and function. After a suitable period of time, the concentration of bacteria in the air measured (in units of bacteria per cubic foot) in all of these rooms. Assume the populations are norm- distributed. The following is a summary of the data: x S Carpeted rooms: 184 22.0 Uncarpeted rooms: 175 16.9 19. A 95% confidence interval for the difference in mean bacterial concentration in the air of carpeted ro versus uncarpeted rooms is (use 11 degrees of freedom).
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Chapter1: Combinatorial Analysis
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Transcribed Image Text:### Analysis of Airborne Bacteria in Carpeted vs. Uncarpeted Rooms
In this experiment, researchers investigated whether there is a difference in the amount of airborne bacteria between carpeted and uncarpeted rooms. The study was conducted in rooms that are similar in size and function. Seven rooms were equipped with carpets, while seven other rooms were left uncarpeted. After a suitable period, the concentration of bacteria in the air (measured in units of bacteria per cubic foot) was recorded for each room. The populations are assumed to be normally distributed.
#### Summary of Data
- **Carpeted Rooms:**
- Mean concentration (\( \bar{x} \)): 184 units
- Standard deviation (s): 22.0 units
- **Uncarpeted Rooms:**
- Mean concentration (\( \bar{x} \)): 175 units
- Standard deviation (s): 16.9 units
#### Problem 19: Confidence Interval Calculation
To determine if there is a significant difference in mean bacterial concentration between the two types of rooms, a 95% confidence interval for the difference in means was calculated using 11 degrees of freedom.
##### Provided Options for 95% Confidence Interval:
- \( \boxed{-7.47 \text{ to } 31.47} \)
- \( \boxed{-18.89 \text{ to } 42.89} \)
- \( \boxed{-16.66 \text{ to } 34.66} \)
- \( \boxed{-14.02 \text{ to } 32.01} \)
These intervals estimate the range within which the true difference in mean bacterial concentration between carpeted and uncarpeted rooms lies, with 95% confidence. Each interval above represents a potential range based on different calculations.
Use your statistical knowledge and tools to determine the correct confidence interval for the difference in mean bacterial concentrations.
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