Question

The mayor of a town has proposed a plan for the construction of a new community. A political study took a sample of 800 voters in the town and found that 34 % 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

30%. State the null and alternative hypotheses.

Answer 1

A political strategist wants to test the claim that the percentage of residents who favor construction is more than 30%, so then that represent our claim and needs to be on the alternative hypothesis.

Based on this the correct system of hypothesis are:

Null hypothesis:
`p \leq 0.3`

Alternative hypothesis
`p >0.3`

Explanation:

We have the following info given from the problem:

`n= 800` the random sample of voters selected from the town

`\hat p = 0.34` represent the proportion of residents favored construction

`p_o = 0.30` represent the value desired to test.

A political strategist wants to test the claim that the percentage of residents who favor construction is more than 30%, so then that represent our claim and needs to be on the alternative hypothesis.

Based on this the correct system of hypothesis are:

Null hypothesis:
`p \leq 0.3`

Alternative hypothesis
`p >0.3`

And in order to test this hypothesis we can use a one sample z test for a population proportion and the statistic would be given by:

`z=\frac{\hat p -p_o}{\sqrt{(p_o (1-p_o))/(n)}}` (1)

And with the data given we have:

`z=\frac{0.34 -0.3}{\sqrt{(0.3(1-0.3))/(800)}}=2.469`