Study Ch. 7.3, # 63 71
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1 GOALS: 1. Understand the distribution of the sample mean. 2. Understand that using the distribution of the sample mean with sufficiently large sample sizes enables us to use parametric statistics for distributions that are not normal. Study Ch. 7.3, # d, e use calculator Oct 4 3:50 PM What Do We Know so Far? μ_ = μ σ_ = σ n If there are a number of sample means of a particular sample size, n, what is the distribution of? G. Battaly
2 = Distribution of Population normally distributed easy, already done. What about when the Population is NOT normally distributed? NOT normal As n increases, distribution approaches normal G. Battaly
3 SETUP 1. Click the url: 2. Select POP2. This is skewed right. POPULATION: 1. Eamine the histogram. 2. The population size, N = This population consists of values from 6 to 19 ( ais). It is right skewed. Note the mean (7.999) and standard deviation (1.501) eg: 8.030,0.670 will be different each time G. Battaly
4 For 1000 samples for each eg: 8.030, will be different each time eg: 7.992, will be different each time eg: 8.001, will be different each time For samples for n=30, get G: μ = 35, σ = 42, n.d. a) F: sampling distribution of, n = 9 n.d. = normally distributed b) Can you answer part (a) if the distribution of original variable is unknown? c) Can you answer part (a) if the distribution of original variable is unknown and n=36? Why or why not? G. Battaly
5 G: μ = 35, σ = 42 a) G: n.d. F: sampling distribution of, n = 9 n.d. = normally distributed b) Can you answer part (a) if the distribution of the original variable is unknown? even though can compute Do NOT know the shape of the distribution of c) Can you answer part (a) if the distribution of the original variable is unknown and n=36? Why or why not? G: μ, σ, n large [ > 30] a) Identifiy the distribution of b) Does your answer to part (a) depend on n being large? c) If n < 30, can you still identify the μ, σ G. Battaly
6 G: μ, σ, n large [ > 30] a) Identifiy the distribution of b) Does your answer to part (a) depend on n being large? Yes. We are not given the distribution of the population variable,. Only when n > 30 can we say that is ~ n.d. c) If n < 30, you can still compute the μ, σ but it is meaningless because can NOT identify the distribution (shape). Without a known distribution, cannot use area under curve to interpret as either % or probability a) F: sampling distribution of, n = 4 b) F: sampling distribution of, n = 9 d) F: % of all sample of 4 finishers that finished within e) F: % of all sample of 9 finishers that finished within G. Battaly
7 a) F: sampling distribution of, n = 4 b) F: sampling distribution of, n = 9 d) F: % of all samples of 4 finishers that finished within 5 min of μ = 61 min. Interpret, re: sampling error. e) F: % of all samples of 9 finishers that finished within 5 min of μ = 61 min. Interpret, re: sampling error. a) F: sampling distribution of, n = 4 b) F: sampling distribution of, n = 9 Since n.d., can sketch distribution. d) F: % of all sample of 4 finishers that finished within e) F: % of all sample of 9 finishers that finished within G. Battaly
8 a) F: sampling distribution of, n = 4 b) F: sampling distribution of, n = 9 Since n.d., can find areas under the normal curve, and interpret as %. d) F: % of all sample of 4 finishers that finished within normalcdf(,,, ) = or % e) F: % of all sample of 9 finishers that finished within normalcdf(,,, ) = or % a) F: sampling distribution of, n = 4 b) F: sampling distribution of, n = 9 Since n.d., can find areas under the normal curve, and interpret as %. d) F: % of all sample of 4 finishers that finished within normalcdf(56,66,61,4.5) = or 73.35% (table:73.30%) z = μ σ Not required when using calculator. e) F: % of all sample of 9 finishers that finished within When using the table, need to find z score, then area in tail, then subtract from 1. normalcdf(56,66,61,3) = or 90.44% (table: 90.50%) G. Battaly
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