Answer:
[tex]z=\frac{0.75 -0.72}{\sqrt{\frac{0.72(1-0.72)}{900}}}=2.00[/tex]
Now we can calculate the p value. Since is a bilateral test the p value would be:
[tex]p_v= P(Z>2) =0.0228[/tex]
Since the p value is lower than the significance level of 0.05 we have enough evidence to conclude that the true proportion of residents favored annexation is higher than 0.72 or 72%
Step-by-step explanation:
Information given
n=900 represent the random sample selected
[tex]\hat p=0.75[/tex] estimated proportion of residents favored annexation
[tex]p_o=0.72[/tex] is the value that we want to test
represent the significance level
z would represent the statistic
[tex]p_v[/tex] represent the p value
Hypothesis to test
The political strategist wants to test the claim that the percentage of residents who favor annexation is above 72%.:
Null hypothesis:[tex]p\leq 0.72[/tex]
Alternative hypothesis:[tex]p > 0.72[/tex]
The statistic for this case is given by:
[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)
Replacing the data given we got:
[tex]z=\frac{0.75 -0.72}{\sqrt{\frac{0.72(1-0.72)}{900}}}=2.00[/tex]
Now we can calculate the p value. Since is a bilateral test the p value would be:
[tex]p_v= P(Z>2) =0.0228[/tex]
Since the p value is lower than the significance level of 0.05 we have enough evidence to conclude that the true proportion of residents favored annexation is higher than 0.72 or 72%
