In the binomial distribution, as the probability of a \"+\" or \"-\" outcome dis
ID: 3217839 • Letter: I
Question
In the binomial distribution, as the probability of a "+" or "-" outcome distribution of probabilities for all possible outcomes always becomes more and more symmetrical. In the sign test, the p value associated with a given number of "+" outcomes will be the same as p value associated with the same number of "-" outcomes, when the test is two-tailed. In the sign test, when the obtained result is exactly what would be expected by chance (like 9 success out of 18 trials when P = .50), the p value (assuming you're doing a two-tailed test) can sometimes be greater than 1.00. 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 distinct possible outcomes (e.g., number of heads out of N) that allow rejection of H_0 must decrease. In the sign test, if N decreases and the size of the effect of the independent variable decreases of a strength, the probability of a Type II error decreases.Explanation / Answer
C) True : When we come across a similar situation repeatedly & are interested in success(one of the two outcomes) , then the total number of successes may follow a binomial distribution.Of course, a binomial distribution must satisfy certain conditions such as the probability of success must remain the sameduring the experiment, and the outcome of an eventmust not influence the outcomeof any successive event.
when the probability of success p is not very close to 0 or 1 and the number of trials is large, then the normal distribution can be a good approximation to the binomial distribution.The normal approximation to the binomial distributionis particularly useful in problemswhere formula for the binomial distributon is to be used repeatedly to obtain the values of several different terms.
D) True : In a sign test p value associated with the fiven number of + & - outcomes in atwo tailed test always remains the same. If n>10 , normal approximation to the binomial distribution is satisfied.Sign test is applicable on the assumption that we are dealing with the population having a continuous symmetric distribution. A s such the probability of getting a value less than the mean 0.5 is same as thet of greater than 0.5.
E) False : As P =9/18 = 0.5 & X is 9 = No. of successes, then Z will become 0 , for it p value is 0.5 , it can not be greater than 1 as it is the probability.
F) False: Actually no. of heads & No. of tails are approximately same as N= 15 to 20, large enough , follows normal distribution which is symmetric.
G) False : Type II error mean accepting H0 when it is false.So if N decreases & the size of the effect of independent variable also decreases then probability of type II error = 1-alpha also increases. Therefore there will be more chances of accepting null hypothesis.
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