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 52% 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 above 49%. Determine the P-value of the test statistic. Round your answer to four decimal places.

Answer 1

Solution :

This is the right tailed test .

The null and alternative hypothesis is

H0 : p =0.49

Ha : p >0.49

= 0.52

P0 = 0.49

1 - P0 = 1-0.49=0.51

Test statistic = z

= - P0 / [P0 * (1 - P0 ) / n]

= 0.52-0.49/ [(0.49*051) / 1600]  

Z= 2.40

P(z > 2.40 ) = 1 - P(z < 2.40) =1-0.9918=0.0082

P-value = 0.0082