A researcher wants to know whether the acidity of rain (pH) near Houston, Texas, is significantly different from that near Chicago, Illinois. He randomly selected 12 rain dates in Texas and 14 rain dates in Illinois and obtains the following data: Texas Illinois 4.69 5.10 4.40 4.69 5.22 4.46 4.22 4.64 4.93 4.65 4.54 4.35 5.22 4.76 4.69 4.40 4.25 5.14 4.75 4.63 4.11 4.71 4.45 4.49 4.36 4.52 Does the evidence suggest that there is a difference in the pH of rain in Chicago and Houston? Use a 5% level of significance.

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### Analyzing the pH Levels of Rainfall in Houston, Texas and Chicago, Illinois

A researcher conducted a study to determine if the acidity of rain (measured through pH levels) near Houston, Texas, is significantly different from that near Chicago, Illinois. For this study, the researcher randomly selected 12 rain dates in Texas and 14 rain dates in Illinois and recorded the pH levels of the rain. The collected data is presented in the table below:

#### Data Collected:
| Texas | Illinois | | Texas | Illinois  |
|-------|----------|----|-------|----------|
| 4.69  | 5.10     |    | 4.69  | 4.69     |
| 5.22  | 4.46     |    | 4.22  | 4.64     |
| 4.93  | 4.65     |    | 4.54  | 4.35     |
| 5.22  | 4.76     |    | 4.69  | 4.40     |
| 4.25  | 5.14     |    | 4.75  | 4.63     |
| 4.11  | 4.71     |    | 4.45  | 4.49     |
            |           |             | 4.36  | 4.52     |

#### Analysis Objective:
- **Determine if there is a statistically significant difference in the pH levels of rain between Houston, Texas, and Chicago, Illinois.**
- **Significance Level**: 5% (α = 0.05).

### Interpreting the Data:
1. **Observation Distribution**:
   - **Texas** has 12 observations ranging from 4.11 to 5.22 in pH levels.
   - **Illinois** has 14 observations with pH levels ranging from 4.22 to 5.14.
   
2. **pH Level Explanation**:
   - The pH scale ranges from 0 to 14, with 7 being neutral.
   - Values less than 7 are acidic, while values greater than 7 are alkaline.
   - The collected pH values suggest that rain in both locations is slightly acidic.

### Research Question:
Does the evidence suggest that there is a significant difference in the p
Transcribed Image Text:### Analyzing the pH Levels of Rainfall in Houston, Texas and Chicago, Illinois A researcher conducted a study to determine if the acidity of rain (measured through pH levels) near Houston, Texas, is significantly different from that near Chicago, Illinois. For this study, the researcher randomly selected 12 rain dates in Texas and 14 rain dates in Illinois and recorded the pH levels of the rain. The collected data is presented in the table below: #### Data Collected: | Texas | Illinois | | Texas | Illinois | |-------|----------|----|-------|----------| | 4.69 | 5.10 | | 4.69 | 4.69 | | 5.22 | 4.46 | | 4.22 | 4.64 | | 4.93 | 4.65 | | 4.54 | 4.35 | | 5.22 | 4.76 | | 4.69 | 4.40 | | 4.25 | 5.14 | | 4.75 | 4.63 | | 4.11 | 4.71 | | 4.45 | 4.49 | | | | 4.36 | 4.52 | #### Analysis Objective: - **Determine if there is a statistically significant difference in the pH levels of rain between Houston, Texas, and Chicago, Illinois.** - **Significance Level**: 5% (α = 0.05). ### Interpreting the Data: 1. **Observation Distribution**: - **Texas** has 12 observations ranging from 4.11 to 5.22 in pH levels. - **Illinois** has 14 observations with pH levels ranging from 4.22 to 5.14. 2. **pH Level Explanation**: - The pH scale ranges from 0 to 14, with 7 being neutral. - Values less than 7 are acidic, while values greater than 7 are alkaline. - The collected pH values suggest that rain in both locations is slightly acidic. ### Research Question: Does the evidence suggest that there is a significant difference in the p
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