Question

The mayor of a town has proposed a plan for the construction of a new community. A political study took a sample of 1000 voters in the town and found that 69% 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 65%. Testing at the 0.02 level, is there enough evidence to support the strategist's claim?

Step 1 of 6: State the null and alternative hypotheses.

Step 2 of 6:Find the value of the test statistic. Round your answer to two decimal places.

Step 3 of 6:Specify if the test is one-tailed or two-tailed.

Step 4 of 6:Determine the decision rule for rejecting the null hypothesis, H0

Step 5 of 6:Make the decision to reject or fail to reject the null hypothesis

Step 6 of 6:State the conclusion of the hypothesis test

Answer 1

Given that A political study took a sample of n=1000 voters in the town and found that = 69% of the residents favored construction.

The political strategist wants to test the claim that the percentage of residents who favor construction is more than p = 65%.

Based on the claim the hypotheses are:

Ho: Po=0.65

Ha: Po>0.65

we need to check the requirements to run a Z test which is:

if N*Po(1-Po) >=10 and sample is randomly taken then the Z test can be conducted.

so, 1000*(0.65)*(1-0.65) =227.5 and also the sample is randomly taken then we can conduct the Z test.

Test Statistic:

it is calculated as:

Z= 2.65

Test:

Based on the hypothesis we conduct a right-tailed test,

Decision rule/ Rejection region:

At 0.02 the critical value for Zc is computed using excel formula for normal distribution as:

The formula used in excel is =NORM.S.INV(0.98) this results in Zc as 2.05

So, reject Ho if Z> Zc =2.05

P-value:

The p-value for the test can also be computed using excel formula for normal distribution at Z score calculated above as:

The formula used is =1-NORM.S.DIST(2.65, TRUE) which gives P-value as 0.0040

Decision:

Since P-value is less than 0.02 and Z>Zc hence we can reject the null hypothesis Ho.

Conclusion:

Since we reject the null hypothesis at 0.02 level of significance hence we can conclude that there is sufficient evidence to support the claim that the percentage of residents who favor construction is more than 65%.