SOLUTION: The mayor of a town has proposed a plan for the annexation of a new community. A political study took a sample of 1500 voters in the town and found that 42% of the residents favore

Algebra ->  Probability-and-statistics -> SOLUTION: The mayor of a town has proposed a plan for the annexation of a new community. A political study took a sample of 1500 voters in the town and found that 42% of the residents favore      Log On


   

Question 1198265: The mayor of a town has proposed a plan for the annexation of a new community. A political study took a sample of 1500 voters in the town and found that 42% of the residents favored annexation. Using the data, a political strategist wants to test the claim that the percentage of residents who favor annexation is under 45%. Testing at the 0.02 level, is there enough evidence to support the strategist's claim?
Step 2 of 7: Find the value of the test statistic. Round your answer to two decimal places.
Answer by proyaop(69) About Me  (Show Source):
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**1. Calculate the Standard Error**
* **Standard Error (SE) = √(p̂ * (1 - p̂) / n)**
* where:
* p̂ = sample proportion (0.42)
* n = sample size (1500)
* **SE = √(0.42 * (1 - 0.42) / 1500)**
* **SE ≈ 0.0127**
**2. Calculate the Test Statistic (z-score)**
* **z = (p̂ - p0) / SE**
* where:
* p̂ = sample proportion (0.42)
* p0 = hypothesized population proportion (0.45)
* SE = standard error (0.0127)
* **z = (0.42 - 0.45) / 0.0127**
* **z ≈ -2.36**
**Therefore, the value of the test statistic (z-score) is approximately -2.36.**