Suppose that we want to see if the probability of being left-handed is different

Question

Suppose that we want to see if the probability of being left-handed is different for men than it is for women. And suppose that 511 students in this class each test this hypothesis at the 2% significance level using their own personalized class data set.

(a) If the probability of being left-handed is in fact different for men than for women, how many students (on average) would fail to reject the null hypotheis? (Assume that each student does the analysis correctly.)

(b) If the probability of being left-handed is in fact the same for men as it is for women, how many students (on average) would reject the null hypothesis, and falsely conclude that the probability of being left-handed is different for men than for women? (Assume that each student does the analysis correctly.)

a)(A) 26 (B) 5 (C) 506 (D) 10 (E) 485 (F) 0 (G) Impossible to tell becaue the probability of Type I error is unknown. (H) Impossible to tell becaue the probability of Type II error is unknown. (I) 501 Problem

b)(A) 501 (B) Impossible to tell becaue the probability of Type II error is unknown. (C) 5 (D) 0 (E) 506 (F) 26 (G) 10 (H) 485 (I) Impossible to tell becaue the probability of Type I error is unknown.

Explanation / Answer

a) d) or 2% of 511 as it also the type-1 error and for b) B as the answer is Type-2 error but that is unknown and thus it is impossible to tell.

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