We want to test whether two randomly selected polls are different (assume sample size >30). The first has a result of 41% and the second has a result of 51%. While in the field, we are told that the standard error is 3% (not margin of error). Your boss, who is running for re-election, needs to know right away whether they are different (and you've left your iPad and t distribution tables at home). For your margin of error, you'll need to come up with a critical t-score on the fly, so you can calculate your margin of error (remember you Rule of Thumb about an unusual t-/z-score). Based on these finding you tell your boss: A. The 95% confidence interval for each poll result is about 38%-44% vs. 48%-54%; the polls are not likely to be statistically significant. B. The 95% confidence interval for each poll result is about 38%-44% vs. 48%-54%, the polls are likely to be statistically significant. C. You cannot make any decision at all because the value of the t-score is not available. D. Cannot make any decision at all because the distribution of the population is unknown. E. The 95% confidence interval for each poll result is about 35%-47% vs. 45%-57%, the polls are NOT likely to be statistically significant. F. The 95% confidence interval for each poll result is about 35%-47% vs. 45%-57%, the polls are likely to be statistically significant. G. You cannot make any decision at all because statistics is a difficult and confusing art. There is a forum posted answer for this question, but I don't believe it's correct and am confused. Since the intervals overlap, shouldn't that indicate NO significance. I've also seen this question answered where the answer was C. because there is no T-score. I find that an odd choice for such a long question.
Compound Probability
Compound probability can be defined as the probability of the two events which are independent. It can be defined as the multiplication of the probability of two events that are not dependent.
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Probability theory is a branch of mathematics that deals with the subject of probability. Although there are many different concepts of probability, probability theory expresses the definition mathematically through a series of axioms. Usually, these axioms express probability in terms of a probability space, which assigns a measure with values ranging from 0 to 1 to a set of outcomes known as the sample space. An event is a subset of these outcomes that is described.
Conditional Probability
By definition, the term probability is expressed as a part of mathematics where the chance of an event that may either occur or not is evaluated and expressed in numerical terms. The range of the value within which probability can be expressed is between 0 and 1. The higher the chance of an event occurring, the closer is its value to be 1. If the probability of an event is 1, it means that the event will happen under all considered circumstances. Similarly, if the probability is exactly 0, then no matter the situation, the event will never occur.
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