Question

The mayor of a town has proposed a plan for the construction of an adjoining community. A political study took a sample of 1000 voters in the town and found that 60% of the residents favored construction. Using the data, a political strategist wants to test the claim that the percentage of residents who favor construction is more than 56%. Find the value of the test statistic. Round your answer to two decimal places.

Answer 1

5.13

Explanation:

Number of sampled workers= n= 1000

Percentage of residents favouring construction= p' = 60% = 60/100= 0.6.

Testing the claim that the percentage of people favouring the construction is more than 56%= p= 56/100 = 0.56.

To calculate the test statistics we use the formula below;

Test statistics= √n (p' - p)/ √[p×(1-p)] -----------(1).

Substituting the value into equation (1) above, we have;

Test statistics= √1000 (0.6-0.56) / √[0.56×(1-0.56)]

Test statistics= (31.62)(0.04) / √0.5(0.44) = 1.2648/ 0.2464

Test statistics= 5.13312

= 5.13 (to 2 decimal places)