Answer:
Step-by-step explanation:
Hello!
The hypothesis is that less than 45% of the residents favor annexation of a new community.
The parameter of interest is the population proportion of residents that favor the annexation of a new community.
The hypotheses are:
H₀: p ≥ 0.45
H₁: p < 0.45
α: 0.01
After surveying 260 voters, the mayor conducted a hypothesis test and failed to reject the null hypothesis.
This means that at a significance level of 1%, the mayor can conclude that at least 45% of the residents favor annexation of a new community. The mayors claim is not correct.
There is no information on the sample proportion, but let's say, for example, that of the 260 voters surveyed, 160 voted on the favor of the annexation of the new community.
The statistic to use for the test is:
[tex]Z= \frac{'p-p}{\sqrt{\frac{p(1-p)}{n} } }[/tex]≈N(0;1)
'p is the sample proportion
'p= x/n= 135/260= 0.52
The statistic under the null hypothesis is:
[tex]Z_{H_0}= \frac{0.52-0.45}{\sqrt{\frac{0.45*0.55}{260} } }[/tex]= 2.27
This test is one-tailed to the left and the p-value is also one-tailed in the same direction, I've calculated it:
p-value: 0.0116
Since the p-value is less than the significance level α: 0.01, the decision is to not reject the null hypothesis.
I hope it helps!
