Question

The mayor of a town has proposed a plan for the annexation of an adjoining community. A political study took a sample of 1600 voters in the town and found that 38% 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 41%. 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 1

Test statistic = -2.44

There is enough evidence to support the strategist's claim.

Explanation:

H0 : p = 0.41

H1 : p < 0.41

pˆ = 0.38

Test statistic :

z=pˆ−p/√p(1−p)/n

Z = (0.38 - 0.41) / √(0.41(1 - 0.41) / 1600

Z = - 0.03 / √0.0001511875

Z = - 0.03 / 0.0122958

Z = - 2.4399

Test statistic = -2.44

The Pvalue :

P(Z < -2.44) = 0.0073436

α - level = 0.02

If Pvalue < α ; Reject H0

0.0073436 < 0.02 ; We reject H0

Since Pvalue < α ; Hence, There is enough evidence to support the strategist's claim.