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Lecture 9

Bio2244 Lecture 9,10,11 and 12.docx

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Biology 2244A/B
Angela White

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Lecture 9, 10, 11, 12 Normal as Approximation to Binomial Distribution  PROBABLITIES - Requirements o SRS o Conditions for binomial distribution satisfied o Np>=5, nq>=5 - Notation for proportions o P = probability in entire population o P-hat = sample proportion of x successes in sample size n o Q-hat = sample proportion of failures - Point estimate o Single value used to approximate population parameter o It is P-hat!!! Confidence Intervals - Range of values used to estimate true value of population parameter - Confidence level = 1 – alpha (alpha is significance level) o Called degree of confidence o Proportion of times confidence interval contain population parameter Critical Value - Notation o Z(a/2) is positive z-value that separate area of a/2 in right tail of standard normal distribution - For confidence interval o Ex. 95 percent  Alpha is 0.05  Divided in left tail and right tail is 0.025  From the left side of the graph, probability is 0.9750  Find z-score corresponding = 1.96 Margin of Error - When data from SRS used to estimate population proportion - E (margin of error) maximum difference between observed sample proportion p-hat and true population proportion p - Confidence interval o P-hat – E < p-hat < p-hat + E o Confidence level is expression P-hat plus/minus E o Procedure (normal as an approx
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