The faculty senate at a large university wanted to know what proportion of the students thought foreign language classes should be required for everyone. the statistics department offered to cooperate in conducting a survey, and a simple random sample of 500 students was selected from all the students enrolled in statistics classes. a survey form was sent by email to these 500 students. for parts (a) to (c) discuss the extent to which the specified type of bias would be likely to occur in this survey: (a). selection bias. (b). non response bias. (c). response bias. (d). which of these three types of bias do you think would be the most serious? explain.

a) The act of selecting a sample of students that are enrolled in statistics classes exclusively is a kind of non-random selection, and may contribute for the selection bias to happen since this sample population isn't representative when related to all the students enrolled in this large university.

b) The non-response bias could happen when, from the 500 students sample, some of them might not be able to answer to the survey sent on their email, or simply chose not to answer it, declining to participate. With less answers, the survey becomes less representative.

c) The response bias could happen if students answer to their surveys in an innacurate way, usually if they support their opinion on personal beliefs that aren't always shared by the rest of the sample population.  Since the aim of the survey is to know the students' opinion on the foreign language classes topic, it is expected that response bias happens, having in mind that opinion is a particular thought of each individual.

d) The most serious bias is the selection bias, since the validity of the whole research would be compromised if the sample population isn't representative of the group you aim to study. Without the correct representation of the aim group, the results from the survey are meaningless.

f(2x−x2)=−3x2+6x−1

step-by-step explanation:

set up the composite function and evaluate.

f(2x−x2)=−3x2+6x−1

8

step-by-step explanation: