Question

The mayor of a town has proposed a plan for the construction of an adjoining community. A political study took a sample of 1400 voters in the town and found that 61 % 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 not equal to 64 % . Testing at the  0.01 level, is there enough evidence to support the strategist's claim?

State the null and alternative hypotheses.

Find the value of the test statistic. Round your answer to two decimal places.

Specify if the test is one-tailed or two-tailed.

Determine the P-value of the test statistic. Round your answer to four decimal places.

Identify the value of the level of significance.

Make the decision to reject or fail to reject the null hypothesis.

State the conclusion of the hypothesis test.

Answer 1

Solution:

Given:

p = 0.64

n = 1400

We have to test the claim that the percentage of residents who favor construction is not equal to 64 %

Part a) State the null and alternative hypotheses.

Vs

Part b) Find the value of the test statistic.

Part c) Specify if the test is one-tailed or two-tailed.

The test is two-tailed. Since H1 is not equal to type.

Part d) Determine the P-value of the test statistic.

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

P-value = 2 X P( Z< -2.34)

Look in z table for z = -2.3 and 0.04 and find corresponding area.

P( Z< -2.34) = 0.0096

thus

P-value = 2 X P( Z< -2.34)

P-value = 2 X 0.0096

P-value =0.0192

Part e) Identify the value of the level of significance.

the level of significance = 0.01

Part f) Make the decision to reject or fail to reject the null hypothesis.

Decision Rule:
Reject H0, if P-value < 0.01 level of significance, otherwise we fail to reject H0

Since P-value =0.0192 > 0.01 level of significance, we fail to reject the null hypothesis H0.

Part g) State the conclusion of the hypothesis test.

At 0.01  level, there is not enough evidence to support the strategist's claim that   the percentage of residents who favor construction is not equal to 64 %