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?

Let p be the population proportion of residents who favor construction.

As per given , we have

Null hypothesis :

Alternative hypothesis :  

Since is right-tailed , so the hypothesis test is a right-tailed z-test.

Also, it is given that , the sample size : n= 900

Sample proportion:

Test statistic : , where n is sample size ,   is sample proportion and p is the population proportion.

P-value (right tailed test)=P(z>2)=1-P(z≤2)     [∵P(Z>z)=1-P(Z≤z)]

  [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%.

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step-by-step explanation:

place r′ so that qr′ is parallel to the tangent.

now we get that ∠r′py=∠pr′q, where y is on the tangent, on the opposite side of p from x.

also, because of the symmetry, ∠r′py=∠qpx.

finally, note that no matter where we place r, as long as it's on the correct arc, we have ∠prq=∠pr′q.

stringing all these equalities together, we end up with ∠prq=∠qpx.

this picture will show how its going to look like.

hope this by jack monhen