STAT 400 Lecture AL1 Spring 2015 Dalpiaz Examples for 7 3 7 4 The sample proportion p x n where x is the number of elements in the sample found to belong to the category of interest the number of successes and n is the sample size E P p p 1 p n Var P SD P p 1 p n A large sample confidence interval for the population proportion p is p z 2 1 p 1 p n Just prior to an important election in a random sample of 749 voters 397 preferred Candidate Y over Candidate Z Construct a 90 confidence interval for the overall proportion of voters who prefer Candidate Y over Candidate Z Upper tail probability 0 25 z 0 005 0 0025 0 001 0 0005 0 674 0 841 1 036 1 282 1 645 1 960 2 054 2 326 2 576 2 807 3 091 3 291 99 5 99 8 99 9 50 0 20 60 0 15 70 0 10 80 0 05 90 0 025 95 0 02 96 0 01 98 Confidence level 99 2 An article on secretaries salaries in the Wall Street Journal reports Three fourth of surveyed secretaries said they make less than 25 000 a year Suppose that the Journal based its results on a random sample of 460 secretaries drawn from every category of business Give a 95 confidence interval for the proportion of secretaries earning less than 25 000 a year The sample size required to obtain a confidence interval for the population proportion n z 2 Always round p with specified margin of error is 2 p 1 p n Conservative Approach up p 0 50 If it is possible that p 0 50 use p 0 50 If it is not possible that p 0 50 use p the closest to 0 50 possible value of p 3 Find the minimum sample size required for the overall proportion of voters who prefer Candidate Y over Candidate Z to within 2 with 90 confidence Assume that no guess as to what that proportion might be is available 4 A television station wants to estimate the proportion of the viewing audience in its area that watch its evening news Find the minimum sample size required to estimate that proportion to within 3 with 95 confidence if a no guess as to the value of that proportion is available b it is known that the station s evening news reaches at most 30 of the viewing audience
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