Question

The mayor of a town has proposed a plan for the construction of an adjoining bridge. A political study took a sample of 1100 voters in the town and found that 81% 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 above 78%. Find the value of the test statistic. Round your answer to two decimal places.

Answer 1

Solution:

Let p be the population proportion.

Claim to be tested is " p is above 78%

i.e. p > 0.78

n = 1100

Let   be the sample proportion.

= 81% = 0.81

Null and alternative hypothesis are

H0 : p = 0.78

H1 : p >  0.78

The test statistic z is

z =   

=  (0.81 - 0.78)/[0.78*(1 - 0.78)/1100]

= 2.40

The value of the test statistic z = 2.40