Question

The mayor of a town has proposed a plan for the construction of a new community. A political study took a sample of 1100 voters in the town and found that 25% 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 22%. State the null and alternative hypotheses.

Answer 1

Answer:

Null Hypothesis: H₀: P>0.22

Alternative hypothesis: H₁:P<0.22

Test statistic  Z = 2.5

 Step-by-step explanation:

Explanation:-

Given size of the sample 'n' =1100

Given data a political study took a sample of 1100 voters in the town and found that 25% of the residents favored construction.

Therefore Given  sample proportion 'p' = 25% = 0.25

Given data a political strategist wants to test the claim that the percentage of residents who favor construction is more than 22%.

Given Population proportion 'P' = 22% = 0.22

Q = 1-p = 1- 0.22=0.78

Given data a political strategist wants to test the claim that the percentage of residents who favor construction is more than 22%

so we choose null hypothesis is

Null Hypothesis: H₀: P>0.22

Alternative hypothesis: H₁:P<0.22

The test of statistic

$Z = \frac{p-P}{\sqrt{\frac{PQ}{n} } }$

$Z = \frac{0.25-0.22}{\sqrt{\frac{0.22 X 0.78}{1100} } }$

Z =   2.5