During the 1990s, the fatality rate for lung cancer was 70 per 100,000 people. After the turn of the century and the establishment of newer treatments and adjustment in public health advertising, a random sample of 10,000 people exhibits only four deaths due to lung cancer. Test at the 0.025 significance level whether these data are proof of a reduced fatality rate for lung cancer.

(a) State the null hypothesis and the alternate hypothesis. (Round your answers to 4 decimal places.)

(b) State the decision rule for 0.02 significance level. (Negative amount should be indicated by a minus sign. Round your answer to 2 decimal places.)

(c) Compute the value of the test statistic. (Negative amount should be indicated by a minus sign. Round your answer to 2 decimal places.)

(d) Test at the 0.02 significance level whether these data are proof of a reduced fatality rate for lung cancer.