a. On average, approximately 10 students would falsely conclude that the probability of being left-handed is different for men and women.
The answer is (G) 10.
b. The answer is (B) Impossible to tell because the probability of Type II error is unknown.
How to determine the number of students
a) If the probability of being left-handed is the same for men and women, and each student correctly performs the analysis, the number of students who falsely conclude that the probability is different for men and women corresponds to the significance level of the test.
In this case, the significance level is 2%.
The significance level represents the probability of making a Type I error, which is rejecting the null hypothesis when it is true.
Therefore, out of 475 students, on average, we would expect 2% of them to falsely conclude that the probability of being left-handed is different for men and women.
Calculating 2% of 475:
0.02 * 475 = 9.5
Since we can't have a fractional number of students, we round to the nearest whole number.
Therefore, on average, approximately 10 students would falsely conclude that the probability of being left-handed is different for men and women.
The answer is (G) 10.
b) If the probability of being left-handed is different for men and women, and each student correctly performs the analysis, the number of students who fail to reject the null hypothesis depends on the power of the test, which is related to the Type II error rate.
However, the information provided does not specify the power of the test or the probability of Type II error.
Therefore, we cannot determine the number of students who would fail to reject the null hypothesis.
The answer is (B) Impossible to tell because the probability of Type II error is unknown.