Step 1 :The null hypothesis expressed in words is the proportion of cancer diagnoses attributable to lung cancer is equal to 27%. The null hypothesis is expressed symbolically as \(H_{0}: p = 0.27\).
Step 2 :The alternative hypothesis expressed in words is the proportion of cancer diagnoses attributable to lung cancer is not equal to 27%. The alternative hypothesis is expressed symbolically as \(H_{a}: p \neq 0.27\).
Step 3 :Since the alternative hypothesis is that the proportion of cancer diagnoses attributable to lung cancer is not equal to 27%, the test is two-tailed. This is because we are looking for a difference in either direction from the claimed proportion.
Step 4 :To sketch a normal sampling distribution and shade the area for the P-value, we would need to know the sample size, the sample mean, and the standard deviation. However, these are not provided in the question.
Step 5 :The final answer is: The null hypothesis in words is 'the proportion of cancer diagnoses attributable to lung cancer is equal to 27%'. In symbols, it is \(H_{0}: p = 0.27\). The alternative hypothesis in words is 'the proportion of cancer diagnoses attributable to lung cancer is not equal to 27%'. In symbols, it is \(H_{a}: p \neq 0.27\). The test is two-tailed.