State $\mathrm{H}_{0}$ and $\mathrm{H}_{\mathrm{a}}$ in words and in symbols. Then determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed. Explain your reasoning. Sketch a normal sampling distribution and shade the area for the P-value.

A report claims that lung cancer accounts for at least $27 \%$ of all cancer diagnoses.

State the null hypothesis in words and in symbols.
The null hypothesis expressed in words is the proportion of cancer diagnoses attributable to lung cancer . The null hypothesis is expressed symbolically as $\mathrm{H}_{0}: \mathrm{p} \nabla \square$.
(Type integers or decimals. Do not round.)

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.