Physicians at a clinic gave what they thought were drugs to 1000 asthma, ulcer, and herpes patients. Although the doctors later learned that the drugs were really placebos, 55% of the patients reported an improved condition. Assume that if the placebo is ineffective, the probability of a patients condition improving is 0.52 For the hypotheses that the proportion of improving is 0.52 against that it is >0.52, find the p-value.
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.
Physicians at a clinic gave what they thought were drugs to 1000 asthma, ulcer, and herpes patients. Although the doctors later learned that the drugs were really placebos, 55% of the patients reported an improved condition. Assume that if the placebo is ineffective, the probability of a patients condition improving is 0.52 For the hypotheses that the proportion of improving is 0.52 against that it is >0.52, find the p-value.
Pedro thinks that he has a special relationship with the number 4. In particular, Pedro thinks that he would roll a 4 with a fair 6-sided die more often than you'd expect by chance alone. Suppose pp is the true proportion of the time Pedro will roll a 4.
(a) State the null and alternative hypotheses for testing Pedro's claim. (Type the symbol "p" for the population proportion, whichever symbols you need of "<", ">", "=", "not =" and express any values as a fraction e.g. p = 1/3)
(b) Now suppose Pedro makes n = 38 rolls, and a 4 comes up 8 times out of the 38 rolls. Determine the P-value of the test:
P-value =
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