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 1400 voters in the town and found that 61% 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% 64 % . Testing at the 0.01 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:

We are given following data values: p = population proportion of the residents favored construction = 0.64

Sample size = n = 1400

Sample proportion of the residents favored construction =

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

( this is not equal to type , hence this is two tailed test)

Part b) Find the value of the test statistic.

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

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

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

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

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.

From above table we get:

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.

We have 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%