STATS 250 Lecture Notes - Lecture 7: Type I And Type Ii Errors, Binomial Distribution, Binomial Test
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STATS 250 Full Course Notes
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Stats 250: introduction to statistics - lecture 7: testing about a population proportion. Continued & learning about the difference in population proportions. Testing hypotheses about a population proportion p when n is small: If n is small (i. e. np0 < 10 or n(1 - p0) < 10), we must go back to the exact distribution for a count x, called the binomial distribution. If x has the binomial distribution bin(n, p), then P(x = k) = (n k)pk(1 - p)n-k, where k = 0, 1, 2, 3, , n. The standard deviation of x is (np(1 - p)) To test the hypothesis h0: p = p0, the count test statistic must be computed. X = the number of successes in the sample size n, which has the bin(n, p0) distribution when h0 is true. This bin(n, p0) distribution is used to compute the p-value for the test. Review of testing hypotheses for different sample sizes:
