Question

The mayor of a town has proposed a plan for the annexation of a new bridge. A political study took a sample of 900900 voters in the town and found that 377% 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 344%. Testing at the 0.020.02 level, is there enough evidence to support the strategist's claim

Answer 1

Hence, we fail to reject the null ;

There is no significant evidence to support the claim that the percentage of residents who favor annexation is over 34%

Explanation:

Given that :

Sample size, n = 900

p = 0.37

p0 = 0.34

H0 : p = 0.34

H1 : p > 0.34

Right tailed test:

Decision region:

Reject Null if ;

Zstatistic > Zcritical

Zcritical at α 0.02 = 2.05

Hence

Reject H0 : if Zstatistic > 2.05

Zstatistic = (p - p0) / sqrt((p0(1-p0))/n)

= (0.37 - 0.34) / sqrt((0.34(1-0.34))/900)

= 1.8999

1.8999 < 2.05

Zstatistic < Zcritical

Hence, we fail to reject the null ;

There is no significant evidence to support the claim that the percentage of residents who favor annexation is over 34%