Question

An owner of a fast food chain stated that he would be willing to build one of his restaurants in a certain city if more than 30% of potential customers indicate they would be likely to come to try the restaurant after it is built. In a sample of 600 potential customers, 220 indicated that they would try it. Test whether the owner should build the restaurant. Does this scenario represent a confidence interval or a hypothesis test?

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: p = 0.3
Alternative Hypothesis, Ha: p > 0.3

Rejection Region
This is right tailed test, for α = 0.05
Critical value of z is 1.64.
Hence reject H0 if z > 1.64

Test statistic,
z = (pcap - p)/sqrt(p*(1-p)/n)
z = (0.3667 - 0.3)/sqrt(0.3*(1-0.3)/600)
z = 3.57

P-value Approach
P-value = 0.0002
As P-value < 0.05, reject the null hypothesis.

Restaurant should be built
This is a scenario of hypothesis test