A method currently used by doctors to screen women for possible breast cancer fails to detect cancer in 15% of the women who have the disease. A new method has been developed that researchers hope will be able to detect cancer more accurately. A random sample of 70 women known to have breast cancer were screened using the new method. Of these, the new method failed to detect cancer in 8.

a. (10 points) At a significance level of 0.01, run a hypothesis testing for the new method claim that the researchers hope to detect cancer more accurately. Please include TI-84 commands.

b. (5 points) According to your conclusion in part a, what type of error can occur?

c. (8 points) What would be the consequences of this type of error?