The mayor of a town has proposed a plan for the construction of an adjoining bridge. A political study took a sample of 1300 voters in the town and found that 38% 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 over 35%. Testing at the 0.05 level, is there enough evidence to support the strategist's claim?

We reject H₀, we have enough evidence to support the claim that the porcentage of residents who favor construction is over 35%

Step-by-step explanation:

Sample size    n  = 1300

Sample  proportion   p = 38 %      =  0,38   then  q = 62%   q =  0,62

The size of the sample is enough to consider the binomial distribution can approximate to normal distribution

p*n  =  1300*0,38     q*n  =  1300*0,62  

p*n > 10    q*n> 10

Population proportion   35%        p₀  = 35 %    p₀  = 0,35

Hypothesis Test :

Null Hypothesis                                         H₀           p = p₀

Alternative Hypothesis                             Ha           p  > p₀

The hypothesis test is a one-tail test to the right

Significance Level   α  =  0,05  we go to z-table and find z(c)

z(c) =  1,64

To calculate  z(s)

z(s)  =  (  p  -  p₀ ) / √ p*q/ n

z(s)  =  0,38  -  0,35  / √ ( 0,38 * 0,62) / 1300

z(s)  =  0,03 / 0,013

z(s)  =  2,307

Comparing  z(c)  and  z(s)

z(s)  >  z(c)      2,307  >  1,64

z(s)  is in the rejection region for H₀, we must reject H₀

We have enough evidence to support the claim