Question

The mayor of a town has proposed a plan for the annexation of an adjoining bridge. A political study took a sample of 900 voters in the town and found that 42% 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 not equal to 46%. Testing at the 0.05 level, is there enough evidence to support the strategist's claim?

Step 1 of 7:

State the null and alternative hypotheses. i.e Ho and Ha

t value

p value

sufficient or not

one tail or two tail

Answer 1

Solution:

This a two- tailed test.

The null and alternative hypothesis is,

Ho: p = 0.46

Ha: p 0.46

Test statistics

z = ( - ) / *(1-) / n

= ( 0.42 - 0.46) / (0.46*0.54) / 900

= -2.408

P-value =2 * P(Z < z )

= 2 * P(Z < -2.408 )

= 2 * 0.0080

= 0.0160

The p-value is p = 0.0160, and since p = 0.0160 < 0.05, it is concluded that the null hypothesis is rejected.

Conclusion:

It is concluded that the null hypothesis Ho is rejected. Therefore, there is sufficient evidence to claim that the percentage of residents who favor annexation is not equal to 46%. at the α = 0.05 significance level.