document.write( "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?\r
\n" ); document.write( "\n" ); document.write( "Step 2 of 7: Find the value of the test statistic. Round your answer to two decimal places.
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Algebra.Com's Answer #848486 by proyaop(69)\"\" \"About 
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**1. Calculate the Standard Error**\r
\n" ); document.write( "\n" ); document.write( "* **Standard Error (SE) = √(p̂ * (1 - p̂) / n)**
\n" ); document.write( " * where:
\n" ); document.write( " * p̂ = sample proportion (0.42)
\n" ); document.write( " * n = sample size (1500)\r
\n" ); document.write( "\n" ); document.write( "* **SE = √(0.42 * (1 - 0.42) / 1500)**
\n" ); document.write( "* **SE ≈ 0.0127**\r
\n" ); document.write( "\n" ); document.write( "**2. Calculate the Test Statistic (z-score)**\r
\n" ); document.write( "\n" ); document.write( "* **z = (p̂ - p0) / SE**
\n" ); document.write( " * where:
\n" ); document.write( " * p̂ = sample proportion (0.42)
\n" ); document.write( " * p0 = hypothesized population proportion (0.45)
\n" ); document.write( " * SE = standard error (0.0127)\r
\n" ); document.write( "\n" ); document.write( "* **z = (0.42 - 0.45) / 0.0127**
\n" ); document.write( "* **z ≈ -2.36**\r
\n" ); document.write( "\n" ); document.write( "**Therefore, the value of the test statistic (z-score) is approximately -2.36.**
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