Question

A statistics student finds herself struggling with a newspaper article stating that only eighteen percent of her community is against the construction of a new soundproofing wall in her neighborhood. She goes door to door, asking 200 of her neighbors whether they are for or against the wall. She finds that twenty five percent of her neighborhood is against constructing the wall. If she chooses a 1% significance level, can she safely conclude that the actual percent of people against building the new soundproofing wall is higher than 18%?

Please type in the Critical Value(s) , the Test Statistic , and the result of the test

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: p = 0.18
Alternative Hypothesis, Ha: p > 0.18

Rejection Region
This is right tailed test, for α = 0.01
Critical value of z is 2.326.
Hence reject H0 if z > 2.326

Test statistic,
z = (pcap - p)/sqrt(p*(1-p)/n)
z = (0.25 - 0.18)/sqrt(0.18*(1-0.18)/200)
z = 2.58

reject the null hypothesis.