Answer:
The statistic for this test is given by:
[tex]z=\frac{0.75 -0.72}{\sqrt{\frac{0.72(1-0.72)}{1200}}}=2.31[/tex]
Step-by-step explanation:
Information given
n=1200 represent the random sample taken
[tex]\hat p=0.75[/tex] estimated proportion of residents who favored annexation.
[tex]p_o=0.72[/tex] is the value that we want to test
z would represent the statistic
System of hypothesis
we want to test if the percentage of residents who favor annexation is above 72%, so then the system of hypothesis are:
Null hypothesis:[tex]p\leq 0.72[/tex]
Alternative hypothesis:[tex]p > 0.72[/tex]
The statistic for this case is given from the one sample proportion test:
[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)
Replacing the info given we got:
[tex]z=\frac{0.75 -0.72}{\sqrt{\frac{0.72(1-0.72)}{1200}}}=2.31[/tex]
