This assignment will be submitted in two parts. Some answers will be submitted directly to the online homework system, and these questions will include a note saying ( WebWorkiR ) at the start. Other questions will be submitted on paper, in class. These questions will include a note saying ( On-Paper ) at the start.

A medical research team wishes to assess the usefulness of a particular symptom in the diagnosis of a particular disease. In other words they would like to use the presence of a particular symptom as an indicator of the disease. In a random sample of patients with the disease, did not report having the symptom. In an independent random sample of subjects without the disease, did not report that they had the symptom.

Part (a) ( On-Paper ) Explain what a false positive would be using descriptive words, in the context of this example.

Part (b) ( WebWorkiR ) What is the probability of making a false positive, based on the sample data? Report your answer as a proportion, rounded to three decimal places.

Part (c) ( On-Paper ) Explain what a false negative would be using descriptive words, in the context of this example.

Part (d) ( WebWorkiR ) What is the probability of making a false negative, based on the sample data? Report your answer as a proportion, rounded to three decimal places.

Part (e) ( On-Paper ) Explain what the sensitivity of the test means using descriptive words, in the context of this example.

Part (f) ( WebWorkiR ) What is the sensitivity of this test, based on the sample data? Report your answer as a proportion, rounded to three decimal places.

Part (g) ( On-Paper ) Explain what the specificity of the test means using descriptive words, in the context of this example.

Part (h) ( WebWorkiR ) What is the specificity of this test, based on the sample data? Report your answer as a proportion, rounded to three decimal places.

Part (i) ( On-Paper ) Do you notice any connection between a false positive and the specificity? Any connection between a false negative and the sensitivity? Please comment on connection you observe between the two.

Part (j) ( On-Paper ) Explain what the positive predictive value (PPV) and negative predictive value (NPV) are using descriptive words, in the context of this example. Explain the value of these, contrasting them with the sensitivity/specificity.

Part (h) ( On-Paper ) BONUS: Answer this question if you like. It is not worth any marks, although it is worth you thinking about here. Suppose one would like to estimate the PPV or NPV. Why is it not possible, based on the data available? What other piece of information is required in order to estimate the PPV or NPV?