Question

The mayor of a town has proposed a plan for the annexation of a new community. A political study took a sample of 1600 voters in the town and found that 68% 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 over 65% . Determine the P-value of the test statistic. Round your answer to four decimal places.

Answer 1

SOLUTION:

From given data,

The mayor of a town has proposed a plan for the annexation of a new community. A political study took a sample of 1600 voters in the town and found that 68% 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 over 65% .

= 68% = 68/100 = 0.68

n = 1600

Test hypothesis:

H₀: p = 0.65

H_a: p > 0.65

Test statistics

z = ( - p) / sqrt [ p( 1 - p) / n ]

= (0.68 - 0.65) / sqrt( 0.65* ( 1 - 0.65) / 1600)

= 2.52

p-value = P(Z > z)

= P(Z > 2.52)

= 1 - P(Z < 2.52)

= 1 - 0.99413

= 0.00587

p-value = 0.0059 [Round your answer to four decimal places.]

Please thumbs-up / vote up this answer if it was helpful. In case of any problem, please comment below. I will surely help. Down-votes are permanent and not notified to us, so we can't help in that case.