Respuesta :
Answer:
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: [tex]p \leq 0.3[/tex]
Alternative hypothesis [tex]p >0.3[/tex]
Step-by-step explanation:
We have the following info given from the problem:
[tex] n= 800[/tex] the random sample of voters selected from the town
[tex]\hat p = 0.34[/tex] represent the proportion of residents favored construction
[tex]p_o = 0.30[/tex] 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: [tex]p \leq 0.3[/tex]
Alternative hypothesis [tex]p >0.3[/tex]
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:
[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)
And with the data given we have:
[tex]z=\frac{0.34 -0.3}{\sqrt{\frac{0.3(1-0.3)}{800}}}=2.469[/tex]
