Answer:
There is enough evidence to support the claim that the percentage of residents who favor annexation is more than 47%.
Step-by-step explanation:
We are given the following in the question:
Sample size, n = 1000
p = 47% = 0.47
Alpha, α = 0.05
First, we design the null and the alternate hypothesis
[tex]H_{0}: p = 0.47\\H_A: p > 0.47[/tex]
This is a one-tailed(right) test.
Formula:
[tex]\hat{p} = 51\% = 0.51[/tex]
[tex]z = \dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}}[/tex]
Putting the values, we get,
[tex]z = \displaystyle\frac{0.51-0.47}{\sqrt{\frac{0.47(1-0.47)}{1000}}} = 2.5343[/tex]
Now, we calculate the p-value from the table.
P-value = 0.0056
Since the p-value is lower than the significance level, we fail to accept the null hypothesis and accept the alternate hypothesis.
Thus. the percentage of residents who favor annexation is more than 47%.
Thus, there is enough evidence to support the claim that the percentage of residents who favor annexation is more than 47%.
