The mayor of a town has proposed a plan for the annexation of an adjoining bridge. A political study took a sample of 1600 voters in the town and found that $24 \%$ 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 less than $27 \%$. Testing at the 0.10 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.

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Step 1 ：The question is asking for the value of the test statistic in a hypothesis test. The test statistic is a measure of how far our sample statistic is from the hypothesized population parameter, in terms of standard errors. In this case, we are testing a claim about a population proportion.

Step 2 ：The test statistic can be calculated using the formula: \(Z = \frac{{\hat{p} - p_0}}{{\sqrt{\frac{{p_0 * (1 - p_0)}}{n}}}}\), where \(\hat{p}\) is the sample proportion, \(p_0\) is the hypothesized population proportion, and \(n\) is the sample size.

Step 3 ：In this case, \(\hat{p} = 0.24\) (24% of the residents favored annexation), \(p_0 = 0.27\) (the claim is that the percentage of residents who favor annexation is less than 27%), and \(n = 1600\) (the sample size is 1600 voters).

Step 4 ：Let's plug these values into the formula and calculate the test statistic.

Step 5 ：The calculated value of the test statistic is approximately -2.70. This value is negative because the sample proportion is less than the hypothesized population proportion. This is consistent with the claim that the strategist is testing, which is that the percentage of residents who favor annexation is less than 27%.

Step 6 ：Final Answer: The value of the test statistic, rounded to two decimal places, is \(\boxed{-2.70}\).