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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