Hypotheses Testing and Confidence Intervals
A mathematician applies for a job at a bank. She/he has to complete an aptitude test consisting of n = 8 multiple-choice questions. For each of the questions, the mathematician has to choose between 4 possible answers and only one is correct.
· The bank wants to strongly avoid the unfavorable scenario of hiring an incompetent person while they can live with not hiring a competent person. Write up a pair of suitable hypotheses.
· HR has decided that a mathematician is going to be hired if she/he answers at least 6 questions correctly. Determine the error of type 1 i.e., H0 is rejected despite it being true.
· Construct a test with sensitivity α = 0.05. The mathematician answered 4 questions correctly. Is he going to be hired under this setup?
· If the mathematician answers questions correctly with a probability of 0.85. How large is the probability of the above test for an error of type 2 (H0 is not rejected but is not true)?
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