If the company administers n=10 identical triangle taste tests to this job applicant and if we say that ‘x’ is the number of correct identifications made (in n=10 trials), then the Rejection Region is the “set of values which ‘x’ could assume that will lead us to reject the null hypothesis, and prefer the alternative hypothesis.”
We could choose any Rejection Region we like, but suppose the company decides it should be: 6, 7, 8, 9, or 10. That is, if after an applicant is presented with n=10 triangular taste tests (or 10 trials), she correctly identifies the odd sample at least 6 times, we reject the null hypothesis (that the applicant has no taste sensitivity) and prefer the alternative hypothesis (that the applicant has taste discrimination ability), and we make her an offer of employment as a taster.
(a) With a Rejection Region of 6, 7, 8, 9 or 10, what is the probability of a Type I error? _______________
(b) With a Rejection Region of 6, 7, 8, 9 or 10, what is the probability of a Type II error, if the job applicant has a probability of identifying the odd sample with p = 0.5? _______________
(c) With a Rejection Region of 8, 9 or 10, what is the probability of a Type I error? _______________
(d) With a Rejection Region of 8, 9 or 10, what is the probability of a Type II error, if the job applicant has a probability of identifying the odd sample with p = 0.5? __________
(e) Which Rejection Region would you recommend that the brewing company use? Why?