Answer the following True-False questions. In your write-up, just list the sub-q
ID: 3151684 • Letter: A
Question
Answer the following True-False questions. In your write-up, just list the sub-question letter (A-P) and whether the statement is True or False – no need to restate the question or to justify your answer.
A. If the number of trials in the binomial distribution increases by 1 (and P = .5), the probability of getting either of the most extreme possible outcomes (that is, 0 or N) is cut in half.
B. In the binomial distribution, as the probability of a “+” or “-” outcome differs more and more from .5, the shape of the distribution of probabilities for all possible outcomes always becomes more and more symmetrical.
C. In the sign test, the p value associated with a given number of “+” outcomes will be the same as the p value associated with the same number of “-” outcomes, when the test is two-tailed.
D. In the sign test, when the obtained result is exactly what would be expected by chance (like 7 successes out of 14 trials when P = .50), the p value (assuming you’re doing a two-tailed test) can never be greater than 1.00.
E. In the sign test, if N increases from 15 to 20 and alpha is made less stringent (like from .01 to .05), the number of different possible outcomes that allow rejection of H0 must increase. F. In the sign test, if N decreases and the size of the effect of the independent variable decreases, the probability of a Type II error decreases.
G. In the sign test, as the numerical value of Preal decreases, the power of an experiment must always decrease.
H. As power decreases, the probability of correctly rejecting the null hypothesis decreases.
I. If a researcher fails to reject the null hypothesis, then she must “accept” the null hypothesis.
J. A researcher will always know for sure when she has made a Type I error.
K. If the obtained p value is less than the alpha level, the null hypothesis should be rejected.
L. It is impossible to make a Type II error when you reject the null hypothesis.
M. If a researcher uses a one-tailed test, it will be harder for her to reject the null hypothesis than if she uses a two-tailed test, even if the effect is in not the predicted direction.
N. All else being equal, if the N in the sign test increases, it becomes easier to reject the null hypothesis.
O. In a binomial distribution with 15 trials, increasing the alpha level from .01 to .05 means that fewer of the possible particular outcomes (like number of trials correct) will allow rejection of the null hypothesis.
P. All else being equal, if a researcher increases the likelihood of making a Type I error by increasing the value of alpha, then she is also more likely to make a Type II error.
Explanation / Answer
A. If the number of trials in the binomial distribution increases by 1 (and P = .5), the probability of getting either of the most extreme possible outcomes (that is, 0 or N) is cut in half.
TRUE. [ANSWER]
Note that the probability of n successes in in trials if p = 0.5 is 0.5^n. Hence, if n increases by 1, then it becomes 0.5^(n+1) = 0.5^n (0.5). So, it is multiplied by 0.5, so it is cut in half.
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B. In the binomial distribution, as the probability of a “+” or “-” outcome differs more and more from .5, the shape of the distribution of probabilities for all possible outcomes always becomes more and more symmetrical.
FALSE. It becomes more assymetrical as p becomes farther from p = 0.5. [ANSWER]
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