The CEO of a large electric utility claims that at least 80 percent of his one million customers are very satisfied with the service they receive. A local newspaper surveyed 300 customers randomly. 73 percent said they were very satisfied. The test statistic is (Round answer to two decimal places. Do not write 0.12

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
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Author:Carter
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Chapter10: Statistics
Section10.6: Summarizing Categorical Data
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### Customer Satisfaction Survey Analysis

The CEO of a large electric utility claims that at least 80 percent of his one million customers are very satisfied with the service they receive. A local newspaper surveyed 300 customers randomly. Seventy-three percent of them said they were very satisfied.

#### Problem Statement:

We need to determine the test statistic to verify the CEO's claim based on the survey conducted by the local newspaper.

#### Key Information:

- Claimed satisfaction rate by the CEO: 80% (or 0.80)
- Sample size from the survey: 300 customers
- Satisfaction rate from the survey: 73% (or 0.73)

#### Calculation:

- Use the formula for the test statistic in a proportion test:
  
  \[
  z = \frac{\hat{p} - p_0}{\sqrt{\frac{p_0 (1 - p_0)}{n}}}
  \]

  where:
  - \(\hat{p}\) = sample proportion (0.73)
  - \(p_0\) = claimed proportion (0.80)
  - \(n\) = sample size (300)

#### Instructions:

Calculate the test statistic and round the answer to two decimal places. Ensure to write the answer in the appropriate format (e.g., 0.12 instead of .12).

#### Input Box:

The test statistic is [__________].
Transcribed Image Text:### Customer Satisfaction Survey Analysis The CEO of a large electric utility claims that at least 80 percent of his one million customers are very satisfied with the service they receive. A local newspaper surveyed 300 customers randomly. Seventy-three percent of them said they were very satisfied. #### Problem Statement: We need to determine the test statistic to verify the CEO's claim based on the survey conducted by the local newspaper. #### Key Information: - Claimed satisfaction rate by the CEO: 80% (or 0.80) - Sample size from the survey: 300 customers - Satisfaction rate from the survey: 73% (or 0.73) #### Calculation: - Use the formula for the test statistic in a proportion test: \[ z = \frac{\hat{p} - p_0}{\sqrt{\frac{p_0 (1 - p_0)}{n}}} \] where: - \(\hat{p}\) = sample proportion (0.73) - \(p_0\) = claimed proportion (0.80) - \(n\) = sample size (300) #### Instructions: Calculate the test statistic and round the answer to two decimal places. Ensure to write the answer in the appropriate format (e.g., 0.12 instead of .12). #### Input Box: The test statistic is [__________].
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