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September 23, 2014

September 23, 2014

Posted by **Desire** on Thursday, December 3, 2009 at 10:10am.

Suppose our null hypothesis is that a certain applicant has no ability at all to discern differences in beer samples, and that to her one beer tastes pretty much the same as another. Obviously, the alternative hypothesis states that the applicant does have taste discrimination ability. Our job is to present this person with a series of triangle taste tests with the purpose of collecting data (the number of correct identifications made in a series of trials) which help the brewing company classify the job applicant into one of the two groups.

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? _______________ (3 pts)

(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? _______________ (3 pts)

(c) With a Rejection Region of 8, 9 or 10, what is the probability of a Type I error? _______________ (3 pts)

(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? __________ (3 points)

(e) Which Rejection Region would you recommend that the brewing company use? Why? (1 pt)

- What?? -
**Writeacher**, Thursday, December 3, 2009 at 11:54amLots of copy and paste there -- with no thinking indicated.

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