The proportion of deaths due to lung cancer in males ages 15-64 in England and Wales during the period 1970-1972 was 12%. Suppose that of 20 deaths that occur among male workers in this age group who have worked for at least 1 year in a chemical plant, 5 are due to lung cancer. We wish to determine whether there is a difference between the proportion of deaths from lung cancer in this plant and the proportion in the general population.
Is a one-sided or two-sided test appropriate here?" Explain
I think 2 sided because we have no prior information that the proportion of lung cancer deaths is higher or lower than the general population.
You are correct. A two-sided test would be appropriate in this situation because there is no prior information or assumption made about whether the proportion of lung cancer deaths in the chemical plant is higher or lower than the general population.
In a two-sided test, we are testing for the possibility of a difference in either direction. We want to determine if there is a significant difference in the proportion of lung cancer deaths between the plant workers and the general population, regardless of whether the proportion is higher or lower in the plant workers. Therefore, a two-sided test is the appropriate choice.
To perform the test, we can use statistical hypothesis testing. The null hypothesis would be that there is no difference between the proportion of lung cancer deaths in the plant workers and the general population. The alternative hypothesis would be that there is a difference in the proportions.
We can then calculate the test statistic (for example, z-score) and compare it to the corresponding critical value from a standard normal distribution. If the test statistic falls within the acceptance region, we fail to reject the null hypothesis and conclude that there is no significant difference. If the test statistic falls outside the acceptance region, we reject the null hypothesis and conclude that there is a significant difference between the two proportions.