Question

The mayor of a town has proposed a plan for the construction of a new community. A political study took a sample of 1700 voters in the town and found that 73% 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 70%. 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.

Step 2 of 5 :  Find the value of the test statistic. Round your answer to two decimal places.

Step 3 of 5 : Specify if it is one tailed or two tailed

Step 4 of 5 :  Find the P-value of the test statistic. Round your answer to four decimal places.

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

State the conclusion of the hypothesis test.

Answer 1

Solution:

Given:

n = sample size = 1700

Sample proportion of the residents favored construction  of a new community.

Claim: the percentage of residents who favor construction is more than 70%.

level of significance = 0.05

Step 1 of 5: State the null and alternative hypotheses.

H0: p =0.70 Vs H1: p > 0.70

Step 2 of 5 :  Find the value of the test statistic.

Step 3 of 5 : Specify if it is one tailed or two tailed

This is one tailed test, since claim is more than 0.70, that is right tailed, thus H1 is > type, thus this is one tailed test.

Step 4 of 5 :  Find the P-value of the test statistic.

For right tailed test, P-value is given by:

P-value = P( Z> z test statistic)

P-value = P( Z> 2.70)

P-value = 1 - P( Z < 2.70)

Look in z table for z = 2.7 and 0.00 and find corresponding area.

P( Z< 2.70)= 0.9965

thus

P-value = 1 - P( Z < 2.70)

P-value = 1 - 0.9965

P-value = 0.0035

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

Decision Rule:
Reject null hypothesis H0, if P-value < 0.05 level of significance, otherwise we fail to reject H0

Since P-value = 0.0035 < 0.05 level of significance, we reject null hypothesis H0.

State the conclusion of the hypothesis test.

At 0.05 level of significance, we have sufficient evidence to support the claim that: the percentage of residents who favor construction is more than 70%.