Lung cancer is one of the most spread cancer types and has a proportion p=0.12 of all the cancer diseases. The study was conducted to find out if the proportion is larger for the people, who live near the nuclear station. 250 people with cancer were inspected, 35 of them had lung cancer. Let pns be a proportion of people, who live near the nuclear station and have a lung cancer. Clearly state the null and alternative hypotheses. Calculate the test statistic and the p-value.