Question

The mayor of a town has proposed a plan for the construction of an adjoining community. A political study took a sample of 1200 voters in the town and found that 45% 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 48%. Testing at the 0.01 level, is there enough evidence to support the strategist's claim?

Step 1 of 7 : State the null and alternative hypotheses.

Step 2 of 7: Find the value of the test statistic. Round your answer to two decimal places.

Step 3 of 7: Specify if the test is one-tailed or two-tailed.

Step 4 of 7: Determine the P-value of the test statistic. Round your answer to four decimal places.

Step 5 of 7: Identify the value of the level of significance.

Step 6 of 7: Make the decision to reject or fail to reject the null hypothesis.

Step 7 of 7: State the conclusion of the hypothesis test.

Answer 1

Here we have given that,

n=number of voters in the town = 1200

= Sample proportion of voters in the town found that the residents favoured construction= 45%=0.45.

p=Population proportion of residents who favor constructions= 48%=0.48

Step 1 of 7:

Claim: To check whether the proportion of residents who favor constructions is not equal to 48% ( i.e. 0.48).

The null and alternative hypothesis are as follows,

Versus

where p is the proportion of residents who favor constructions

This is the two-tailed test.

Step 2 of 7:

Now, we can find the test statistic is as follows,

Z-statistics=

       =

         = -2.08

The test statistics is -2.08.

Step 3 of 7:

This is the two-tailed test as our interest is to see the proportion of residents who favor constructions is not equal to 48%.

Step 4 of 7:

Now we find the P-value,

p-value=2* P(Z < z-statistics)  as this is two tailed test

               =2* P( Z < -2.08)

                =2* 0.01876 Using standard normal z table see the value corresponding to the z=-3.36

                =0.0375

The p-value is 0.0375

Step 5 of 7:

= level of significance= 0.05

Step 6 of 7:

Decision:

Here p-value (0.0375) less than (<) 0.05

We reject the Ho (Null Hypothesis)

Step 7 of 7:

Conclusion:

There is sufficient evidence to conclude that the proportion of residents who favor constructions is not equal to 48% ( i.e. 0.48).