Question

The mayor of a town has proposed a plan for the annexation of a new community. A political study took a sample of 10001000 voters in the town and found that 56V% of the residents favored annexation. Using the data, a political strategist wants to test the claim that the percentage of residents who favor annexation is more than 53S%. Find the value of the test statistic. Round your answer to two decimal places.

Answer 1

Test statistics = 1.87

Explanation:

We are given that a political study took a sample of 1000 voters in the town and found that 56% of the residents favored annexation.

And, a political strategist wants to test the claim that the percentage of residents who favor annexation is more than 53%, i.e;

Null Hypothesis,
`H_0` : p = 0.53 {means that the percentage of residents who favor annexation is 53%}

Alternate Hypothesis,
`H_1` : p > 0.53 {means that the percentage of residents who favor annexation is more than 53%}

The test statistics we will use here is;

T.S. =
`\frac{\hat p -p}{\sqrt{(\hat p(1- \hat p))/(n) } }` ~ N(0,1)

where, p = actual percentage of residents who favor annexation = 0.53

`\hat p` = percentage of residents who favor annexation in a sample of

1000 voters = 0.56

n = sample of voters = 1000

So, Test statistics =
`\frac{0.56 -0.53}{\sqrt{(0.56(1- 0.56))/(1000) } }`

= 1.87

Therefore, the value of test statistics is 1.87 .