Question

# The mayor of a town has proposed a plan for the annexation of an adjoining community....

The mayor of a town has proposed a plan for the annexation of an adjoining community. A political study took a sample of 1200 voters in the town and found that 75% 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 above 72%. Determine the decision rule for rejecting the null hypothesis, H0, at the 0.10 level.

N = 1200

P = 0.75

First we need to check the conditions of normality that is, if n*p and n*(1-p)

Both are greater than 5 or not

N*p = 900

N*(1-p) = 300

As both are greater than 5, conditions are met and we can use standard normal z table to identify the decision rule

Here claim is p>0.72

That is it is a right tailed test

Critical value from z table, for 0.1 alpha is 1.28

That is critical value zo = 1.28

So, the decision rule is

Reject Ho, if calculated test statistics z is greater than 1.28

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