MATH SOLVE

4 months ago

Q:
# The mayor of a town has proposed a plan for the construction of a new community. A political study took a sample of 900 voters in the town and found that 75% 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 more than 72%. Testing at the 0.05 level, is there enough evidence to support the strategist's claim?

Accepted Solution

A:

Answer with explanation:Let p be the population proportion of residents who favor construction.As per given , we haveNull hypothesis : [tex]H_0: p\leq0.72[/tex]Alternative hypothesis : [tex]H_a: p>0.72[/tex]Since [tex]H_a[/tex] is right-tailed , so the hypothesis test is a right-tailed z-test.Also, it is given that , the sample size : n= 900Sample proportion: [tex]\hat{p}=0.75[/tex]Test statistic : [tex]z=\dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}}[/tex] , where n is sample size , [tex]\hat{p}[/tex] is sample proportion and p is the population proportion.[tex]\Rightarrow\ z=\dfrac{0.75-0.72}{\sqrt{\dfrac{0.72(1-0.72)}{900}}}\approx2[/tex]P-value (right tailed test)=P(z>2)=1-P(z≤2) [∵P(Z>z)=1-P(Z≤z)][tex]=1-0.9772=0.0228[/tex] [using p-value table of z.]Decision : Since P-value (0.0228) < Significance level (0.05), so we reject the null hypothesis .Thus , we concluded that we have enough evidence at 0.05 significance level to support the strategist's claim that the percentage of residents who favor construction is more than 72%.