Statistical Sciences 1024A/B Chapter Notes - Chapter 20: Simple Random Sample, Standard Deviation, Variance

• School: Western University
• Department: Statistical Sciences
• Course: Statistical Sciences 1024A/B
• Professor: Lori Murray

Document Summary

Assume the units that are measured are from a simple random sample. The srs assumption is more important than the assumption that the measurements follow a. In practice, the normal distribution assumption can be relaxed somewhat. Unless n is really small, it is enough that the distribution by symmetric, and single peaked. Replace the populatio(cid:374) sta(cid:374)dard de(cid:448)iatio(cid:374), (cid:449)ith the sa(cid:373)ple sta(cid:374)dar de(cid:448)iatio(cid:374) s: the populatio(cid:374) sta(cid:374)dard de(cid:448)iatio(cid:374) is a para(cid:373)eter. The sa(cid:373)ple sta(cid:374)dard dei(cid:448)ati(cid:374) s is a(cid:374) est i(cid:373)ate of the populatio(cid:374) sta(cid:374)dard de(cid:448)iatio(cid:374) s is a statistic. The sta(cid:374)dard error: the sta(cid:374)dard dei(cid:448)ati(cid:374) of the sa(cid:373)ple (cid:373)ea(cid:374) is, the sa(cid:373)ple sta(cid:374)dard de(cid:448)iatio(cid:374) (cid:894)the esti(cid:373)ated sta(cid:374)dard de(cid:448)iatio(cid:374)(cid:895) is, this esti(cid:373)ate us also called sta(cid:374)dard error of the sa(cid:373)ple (cid:373)ea(cid:374) Degrees of freedom: the sample variance is . In view of the restriction there are n-1 unknown quantities in difference or n-1 degrees of freedom. Comparing t and standard normal: similarities, symmetric about 0, single peaked, bell-shaped.