STAT 3615 Lecture Notes - Lecture 29: Statistical Inference, Statistic, Sampling Distribution
Document Summary
Chapter 17 behavior of means (sd unknown) Estimate sigma: estimate the population standard deviation sigma with the sample standard deviation, s, s is known to be a good estimate of sigma, s is a statistic calculated from sample data. Conditions for inference: data still needs to be collected randomly and independently. Compare t and z distributions: similarities, bell shaped, symmetrical, centered at 0, differences t distribution is more spread out than z distribution, standard deviation of t distribution > 1, more area in the tails of the t-distribution. Summary: as the degrees of freedom increase, the t-distri(cid:271)utio(cid:374)"s shape gets (cid:272)loser a(cid:374)d (cid:272)loser to a z- distribution, at around n = 30-40 the difference is nearly indistinguishable. Is not extremely skewed: assumptions can be eased if we collect a larger sample. Inference for a single mean (mu: we will look at our confidence intervals and hypothesis tests when mu is our parameter of interest.
