An Industrial Psychologist Constructed a Test Intended to Predict On-The-Job

An industrial psychologist constructed a test intended to predict on-the-job success of applicants for the position of widget inspector. In order to discover how well her test worked, she gave her new test to the first applicants for the job and hired them on probationary status regardless of their test scores. She then counted the number of faulty widgets approved by each applicant during their first week on the job. Below are the test scores and errors in approval for each applicant. $\begin{array}{c}\begin{array}{ccc}&&\text { Faulty Widgets }\\ \underline{\text { plicant} } & \underline{\text { Test Score} } & \underline{ \text { Approved }} \\ 1 & 20 & 2 \\ 2 & 18 & 1 \\ 3 & 17 & 5 \\4 & 16 & 4 \\ 5 & 16 & 3 \\ 6 & 15 & 6 \\ 7 & 15 & 9 \\ 8 & 13 & 5 \\\end{array}\begin{array}{ccc}&&\text { Faulty Widgets }\\ \underline{\text { Applicant }} & \underline{ \text { Test Score} } & \underline{\text { Approved }} \\ 9 & 13 & 12 \\10 & 13 & 8 \\11 & 12 & 10 \\12 & 11 & 7 \\13 & 9 & 14 \\ 14 & 6 & 17 \\ 15 & 4 & 22 \\\end{array}\end{array}$

a. How good is the test?
b. How many faulty widgets would you expect to be approved during the first week on the job by a person who scored 14 on the test?