╨в-╤А╨░╤Б╨┐╤А╨╡╨┤╨╡╨╗╨╡╨╜╨╕╨╡
╨з╤В╨╛ ╤В╨░╨║╨╛╨╡ ╨в-╤А╨░╤Б╨┐╤А╨╡╨┤╨╡╨╗╨╡╨╜╨╕╨╡?
╨в-╤А╨░╤Б╨┐╤А╨╡╨┤╨╡╨╗╨╡╨╜╨╕╨╡ тАФ ╤Н╤В╨╛ ╨╜╨╡╨┐╤А╨╡╤А╤Л╨▓╨╜╨╛╨╡ ╤А╨░╤Б╨┐╤А╨╡╨┤╨╡╨╗╨╡╨╜╨╕╨╡ ╨▓╨╡╤А╨╛╤П╤В╨╜╨╛╤Б╤В╨╡╨╣. ╨Ю╨╜ ╨╕╤Б╨┐╨╛╨╗╤М╨╖╤Г╨╡╤В╤Б╤П, ╨║╨╛╨│╨┤╨░ ╤А╨░╨╖╨╝╨╡╤А╤Л ╨▓╤Л╨▒╨╛╤А╨║╨╕ ╨╝╨╡╨╜╤М╤И╨╡, ╤З╨╡╨╝ ╨╜╨╛╤А╨╝╨░╨╗╤М╨╜╨╛╨╡ ╤А╨░╤Б╨┐╤А╨╡╨┤╨╡╨╗╨╡╨╜╨╕╨╡, ╤Б╨║╨░╨╢╨╡╨╝, ╨╝╨╡╨╜╨╡╨╡ 30. ╨н╤В╨╛╤В ╨╝╨╡╤В╨╛╨┤ ╨╛╨┐╤А╨╡╨┤╨╡╨╗╤П╨╡╤В ╨╜╨╡╤Б╨╛╨╛╤В╨▓╨╡╤В╤Б╤В╨▓╨╕╨╡ ╨╝╨╡╨╢╨┤╤Г ╨▓╤Л╨▒╨╛╤А╨║╨╛╨╣ ╨╕ ╤Б╤А╨╡╨┤╨╜╨╕╨╝╨╕ ╨╖╨╜╨░╤З╨╡╨╜╨╕╤П╨╝╨╕ ╤Б╨╛╨▓╨╛╨║╤Г╨┐╨╜╨╛╤Б╤В╨╕, ╨║╨╛╨│╨┤╨░ ╤Б╤В╨░╨╜╨┤╨░╤А╤В╨╜╨╛╨╡ ╨╛╤В╨║╨╗╨╛╨╜╨╡╨╜╨╕╨╡ ╤Б╨╛╨▓╨╛╨║╤Г╨┐╨╜╨╛╤Б╤В╨╕ ╨╜╨╡╨╕╨╖╨▓╨╡╤Б╤В╨╜╨╛.
╨Ю╨╜ ╨╕╤Б╨┐╨╛╨╗╤М╨╖╤Г╨╡╤В╤Б╤П ╨▓ ╤Б╤В╨░╤В╨╕╤Б╤В╨╕╨║╨╡ ╨┤╨╗╤П ╨╛╨┐╤А╨╡╨┤╨╡╨╗╨╡╨╜╨╕╤П ╨╖╨╜╨░╤З╨╡╨╜╨╕╨╣ ╤Н╨║╤Б╤В╤А╨╡╨╝╨░╨╗╤М╨╜╨╛╨│╨╛ ╨┤╨╛╨▓╨╡╤А╨╕╤В╨╡╨╗╤М╨╜╨╛╨│╨╛ ╨╕╨╜╤В╨╡╤А╨▓╨░╨╗╨░ ╨┤╨╗╤П ╨╜╨╛╤А╨╝╨░╨╗╤М╨╜╨╛╨│╨╛ ╤А╨░╤Б╨┐╤А╨╡╨┤╨╡╨╗╨╡╨╜╨╕╤П ╤Б ╨╜╨╡╨▒╨╛╨╗╤М╤И╨╕╨╝ ╤А╨░╨╖╨╝╨╡╤А╨╛╨╝ ╨▓╤Л╨▒╨╛╤А╨║╨╕. ╨Ъ╨░╨║ ╨╕ ╨╜╨╛╤А╨╝╨░╨╗╤М╨╜╨╛╨╡ ╤А╨░╤Б╨┐╤А╨╡╨┤╨╡╨╗╨╡╨╜╨╕╨╡, ╨в-╤А╨░╤Б╨┐╤А╨╡╨┤╨╡╨╗╨╡╨╜╨╕╨╡ ╨╛╨▒╤А╨░╨╖╤Г╨╡╤В ╤Б╨╕╨╝╨╝╨╡╤В╤А╨╕╤З╨╜╤Г╤О ╨║╨╛╨╗╨╛╨║╨╛╨╗╨╛╨╛╨▒╤А╨░╨╖╨╜╤Г╤О ╨║╤А╨╕╨▓╤Г╤О. ╨Э╨╛ ╤Г ╨в-╨║╤А╨╕╨▓╤Л╤Е ╨▒╨╛╨╗╨╡╨╡ ╤В╨╛╨╗╤Б╤В╤Л╨╡ ╤Е╨▓╨╛╤Б╤В╤Л, ╤З╨╡╨╝ ╤Г ╨║╤А╨╕╨▓╨╛╨╣ ╨╜╨╛╤А╨╝╨░╨╗╤М╨╜╨╛╨│╨╛ ╤А╨░╤Б╨┐╤А╨╡╨┤╨╡╨╗╨╡╨╜╨╕╤П; ╤Н╤В╨╛ ╨╕╨╖╨╛╨▒╤А╨░╨╢╨░╨╡╤В ╨║╤А╨░╨╣╨╜╨╕╨╡ ╨╖╨╜╨░╤З╨╡╨╜╨╕╤П ╨┤╨╛╨▓╨╡╤А╨╕╤В╨╡╨╗╤М╨╜╨╛╨│╨╛ ╨╕╨╜╤В╨╡╤А╨▓╨░╨╗╨░.
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╨Ю╨│╨╗╨░╨▓╨╗╨╡╨╜╨╕╨╡
╨Ъ╨╗╤О╤З╨╡╨▓╤Л╨╡ ╨▓╤Л╨▓╨╛╨┤╤Л
- T-╤А╨░╤Б╨┐╤А╨╡╨┤╨╡╨╗╨╡╨╜╨╕╨╡ ╤П╨▓╨╗╤П╨╡╤В╤Б╤П ╨╝╨╡╤А╨╛╨╣ ╨▓╨╡╤А╨╛╤П╤В╨╜╨╛╤Б╤В╨╕ (p-╨╖╨╜╨░╤З╨╡╨╜╨╕╨╡). ╨Ю╨╜ ╨╕╤Б╨┐╨╛╨╗╤М╨╖╤Г╨╡╤В╤Б╤П ╨┤╨╗╤П ╨╜╨░╤Е╨╛╨╢╨┤╨╡╨╜╨╕╤П ╤Б╤В╨░╤В╨╕╤Б╤В╨╕╤З╨╡╤Б╨║╨╛╨╣ ╨╖╨╜╨░╤З╨╕╨╝╨╛╤Б╤В╨╕, ╨║╨╛╨│╨┤╨░ ╤А╨░╨╖╨╝╨╡╤А ╨▓╤Л╨▒╨╛╤А╨║╨╕ ╨╝╨░╨╗, ╤В. ╨╡. ╨╝╨╡╨╜╤М╤И╨╡ 30, ╤Б ╨╜╨╡╤П╤Б╨╜╤Л╨╝ ╤Б╤В╨░╨╜╨┤╨░╤А╤В╨╜╤Л╨╝ ╨╛╤В╨║╨╗╨╛╨╜╨╡╨╜╨╕╨╡╨╝.
- ╨б╤А╨╡╨┤╨╜╨╡╨╡ ╨╖╨╜╨░╤З╨╡╨╜╨╕╨╡ T-╤А╨░╤Б╨┐╤А╨╡╨┤╨╡╨╗╨╡╨╜╨╕╤П ╨╛╤Ж╨╡╨╜╨╕╨▓╨░╨╡╤В╤Б╤П ╨║╨░╨║ ╨╜╨╛╨╗╤М, ╨░ ╨┤╨╕╤Б╨┐╨╡╤А╤Б╨╕╤П ╨┐╨╛╨╗╤Г╤З╨░╨╡╤В╤Б╤П ╨║╨░╨║ v/(v-2), ╨│╨┤╨╡ v тАФ ╤Б╤В╨╡╨┐╨╡╨╜╤М ╤Б╨▓╨╛╨▒╨╛╨┤╤Л.
- ╨н╤В╨╛╤В ╨╝╨╡╤В╨╛╨┤ ╨╜╨░╤Е╨╛╨┤╨╕╤В ╤Н╨║╤Б╤В╤А╨╡╨╝╨░╨╗╤М╨╜╤Л╨╡ ╨╖╨╜╨░╤З╨╡╨╜╨╕╤П тАФ ╨╜╨╕╨╢╨╜╨╕╨╣ ╨╕ ╨▓╨╡╤А╤Е╨╜╨╕╨╣ ╨┐╤А╨╡╨┤╨╡╨╗╤Л ╨┤╨╛╨▓╨╡╤А╨╕╤В╨╡╨╗╤М╨╜╨╛╨│╨╛ ╨╕╨╜╤В╨╡╤А╨▓╨░╨╗╨░.
╨Ю╨▒╤К╤П╤Б╨╜╨╡╨╜╨╕╨╡ T-╤А╨░╤Б╨┐╤А╨╡╨┤╨╡╨╗╨╡╨╜╨╕╤П ╨▓ ╤Б╤В╨░╤В╨╕╤Б╤В╨╕╨║╨╡
╨г╨╕╨╗╤М╤П╨╝ ╨б╨╕╨╗╨╕ ╨У╨╛╤Б╤Б╨╡╤В ╨┐╤А╨╡╨┤╤Б╤В╨░╨▓╨╕╨╗ T-╤А╨░╤Б╨┐╤А╨╡╨┤╨╡╨╗╨╡╨╜╨╕╨╡ ╨▓ ╤Б╤В╨░╤В╨╕╤Б╤В╨╕╨║╨╡ ╨║╨░╨║ ╨╝╨╡╤В╨╛╨┤ ╨░╨╜╨░╨╗╨╕╨╖╨░ ╨▓╨╡╤А╨╛╤П╤В╨╜╨╛╤Б╤В╨╡╨╣ ╨▓ 1908 ╨│╨╛╨┤╤Г. ╨Ю╨╜ ╨┐╤А╨╕╨╝╨╡╨╜╤П╨╡╤В╤Б╤П ╨║ ╤Б╨╗╤Г╤З╨░╤П╨╝ ╤Б ╨╜╨╡╨▒╨╛╨╗╤М╤И╨╕╨╝ ╤А╨░╨╖╨╝╨╡╤А╨╛╨╝ ╨▓╤Л╨▒╨╛╤А╨║╨╕ ╨╕ ╨╜╨╡╤П╤Б╨╜╤Л╨╝ ╤Б╤В╨░╨╜╨┤╨░╤А╤В╨╜╤Л╨╝ ╨╛╤В╨║╨╗╨╛╨╜╨╡╨╜╨╕╨╡╨╝ (╨╜╨░╤Б╨╡╨╗╨╡╨╜╨╕╨╡).
╨б╨╗╨╡╨┤╤Г╤О╤Й╨╕╨╡ ╤Б╨▓╨╛╨╣╤Б╤В╨▓╨░ T-╤А╨░╤Б╨┐╤А╨╡╨┤╨╡╨╗╨╡╨╜╨╕╤П ╨╛╤В╨╗╨╕╤З╨░╤О╤В ╨╡╨│╨╛ ╨╛╤В ╨┤╤А╤Г╨│╨╕╤Е ╨▓╨╕╨┤╨╛╨▓ ╨▓╨╡╤А╨╛╤П╤В╨╜╨╛╤Б╤В╨╜╤Л╤Е ╤А╨░╤Б╨┐╤А╨╡╨┤╨╡╨╗╨╡╨╜╨╕╨╣:
- ╨в-╤А╨░╤Б╨┐╤А╨╡╨┤╨╡╨╗╨╡╨╜╨╕╨╡ ╨╕╨╗╨╕ ╤Б╤В╤Г╨┤╨╡╨╜╤З╨╡╤Б╨║╨╛╨╡ ╨в-╤А╨░╤Б╨┐╤А╨╡╨┤╨╡╨╗╨╡╨╜╨╕╨╡ ╨╛╨▒╤А╨░╨╖╤Г╨╡╤В ╤Б╨╕╨╝╨╝╨╡╤В╤А╨╕╤З╨╜╤Г╤О ╨║╨╛╨╗╨╛╨║╨╛╨╗╨╛╨╛╨▒╤А╨░╨╖╨╜╤Г╤О ╨║╤А╨╕╨▓╤Г╤О ╤Б ╨▒╨╛╨╗╨╡╨╡ ╤В╨╛╨╗╤Б╤В╤Л╨╝╨╕ ╤Е╨▓╨╛╤Б╤В╨░╨╝╨╕.
- ╨Х╨│╨╛ ╤Б╤А╨╡╨┤╨╜╨╡╨╡ ╨╖╨╜╨░╤З╨╡╨╜╨╕╨╡ ╤А╨░╨▓╨╜╨╛ ╨╜╤Г╨╗╤О.
- ╨Т╨╡╨╗╨╕╤З╨╕╨╜╨░ ╤А╨░╤Б╨┐╤А╨╡╨┤╨╡╨╗╨╡╨╜╨╕╤П ╨║╨╛╨╗╨╡╨▒╨╗╨╡╤В╤Б╤П ╨╝╨╡╨╢╨┤╤Г -тИЮ ╨╕ тИЮ.
- ╨Х╨│╨╛ ╨┤╨╕╤Б╨┐╨╡╤А╤Б╨╕╤П ╨▓╤Л╤З╨╕╤Б╨╗╤П╨╡╤В╤Б╤П ╨║╨░╨║ v/(v-2). ╨Ч╨┤╨╡╤Б╤М v тЙе 2 ╨╕ ‘v’ ╨╛╨▒╨╛╨╖╨╜╨░╤З╨░╨╡╤В ╤Б╤В╨╡╨┐╨╡╨╜╤М ╤Б╨▓╨╛╨▒╨╛╨┤╤Л: ‘Var
╨е╨╛╤В╤П ╤Н╤В╨╛ ╤И╨╕╤А╨╛╨║╨╛ ╨╕╤Б╨┐╨╛╨╗╤М╨╖╤Г╨╡╨╝╤Л╨╣ ╨╝╨╡╤В╨╛╨┤, ╨╡╨│╨╛ ╨║╤А╨╕╤В╨╕╨║╤Г╤О╤В ╨╖╨░ ╨╜╨╡╤В╨╛╤З╨╜╨╛╤Б╤В╤М (╨▓ ╨╜╨╡╨║╨╛╤В╨╛╤А╤Л╤Е ╤Б╨╗╤Г╤З╨░╤П╤Е). ╨Ъ╤А╨╛╨╝╨╡ ╤В╨╛╨│╨╛, ╨┐╤А╨╕ ╨▒╨╛╨╗╤М╤И╨╕╤Е ╤А╨░╨╖╨╝╨╡╤А╨░╤Е ╨▓╤Л╨▒╨╛╤А╨║╨╕ ╨╛╨▒╤Л╤З╨╜╨╛ ╨╗╤Г╤З╤И╨╡ ╨╕╤Б╨┐╨╛╨╗╤М╨╖╨╛╨▓╨░╤В╤М ╨╜╨╛╤А╨╝╨░╨╗╤М╨╜╨╛╨╡ ╤А╨░╤Б╨┐╤А╨╡╨┤╨╡╨╗╨╡╨╜╨╕╨╡.
╨а╨░╤Б╤З╨╡╤В
╨н╤В╨╛╤В ╨╝╨╡╤В╨╛╨┤ ╨▓╨║╨╗╤О╤З╨░╨╡╤В ╨▓ ╤Б╨╡╨▒╤П ╨▓╤Л╤З╨╕╤Б╨╗╨╡╨╜╨╕╨╡ ╨┤╨▓╤Г╤Е ╨╖╨╜╨░╤З╨╡╨╜╨╕╨╣:
тДЦ1 тАУ T-╨┐╨╛╨║╨░╨╖╨░╤В╨╡╨╗╤М
╨д╨╛╤А╨╝╤Г╨╗╨░, ╨╕╤Б╨┐╨╛╨╗╤М╨╖╤Г╨╡╨╝╨░╤П ╨┤╨╗╤П ╨╛╨┐╤А╨╡╨┤╨╡╨╗╨╡╨╜╨╕╤П ╨╖╨╜╨░╤З╨╡╨╜╨╕╤П T-Distribution, ╨▓╤Л╨│╨╗╤П╨┤╨╕╤В ╤Б╨╗╨╡╨┤╤Г╤О╤Й╨╕╨╝ ╨╛╨▒╤А╨░╨╖╨╛╨╝:
╨Ч╨┤╨╡╤Б╤М,
- x╠Д тАФ ╨▓╤Л╨▒╨╛╤А╨╛╤З╨╜╨╛╨╡ ╤Б╤А╨╡╨┤╨╜╨╡╨╡;
- ╬╝ тАФ ╤Б╤А╨╡╨┤╨╜╨╡╨╡ ╨╖╨╜╨░╤З╨╡╨╜╨╕╨╡ ╨│╨╡╨╜╨╡╤А╨░╨╗╤М╨╜╨╛╨╣ ╤Б╨╛╨▓╨╛╨║╤Г╨┐╨╜╨╛╤Б╤В╨╕;
- s тАФ ╤Б╤В╨░╨╜╨┤╨░╤А╤В╨╜╨╛╨╡ ╨╛╤В╨║╨╗╨╛╨╜╨╡╨╜╨╕╨╡;
- n тАФ ╤А╨░╨╖╨╝╨╡╤А ╨▓╤Л╨▒╨╛╤А╨║╨╕.
#2 тАУ ╨б╤В╨╡╨┐╨╡╨╜╤М ╤Б╨▓╨╛╨▒╨╛╨┤╤Л
╨Ф╨╕╤Б╨┐╨╡╤А╤Б╨╕╤П ╨▓╤Л╨▓╨╛╨┤╨╕╤В╤Б╤П ╤Б ╨╕╤Б╨┐╨╛╨╗╤М╨╖╨╛╨▓╨░╨╜╨╕╨╡╨╝ ╤Б╤В╨╡╨┐╨╡╨╜╨╕ ╤Б╨▓╨╛╨▒╨╛╨┤╤Л ╨┤╨╗╤П ╨┤╨░╨╜╨╜╨╛╨│╨╛ ╤А╤П╨┤╨░ ╨┤╨░╨╜╨╜╤Л╤Е. ╨Ю╨╜ ╤А╨░╤Б╤Б╤З╨╕╤В╤Л╨▓╨░╨╡╤В╤Б╤П ╨║╨░╨║ ╤А╨░╨╖╨╝╨╡╤А ╨▓╤Л╨▒╨╛╤А╨║╨╕ ╨╝╨╕╨╜╤Г╤Б 1:
╨┤╤Д = ╨┐ тАУ 1
╨Ч╨┤╨╡╤Б╤М,
- df тАФ ╤Б╤В╨╡╨┐╨╡╨╜╤М ╤Б╨▓╨╛╨▒╨╛╨┤╤Л;
- ┬лn┬╗ тАФ ╤А╨░╨╖╨╝╨╡╤А ╨▓╤Л╨▒╨╛╤А╨║╨╕.
╨Ч╨╜╨░╤З╨╡╨╜╨╕╨╡, ╨┐╨╛╨╗╤Г╤З╨╡╨╜╨╜╨╛╨╡ ╨╕╨╖ ╨┐╤А╨╕╨▓╨╡╨┤╨╡╨╜╨╜╨╛╨╣ ╨▓╤Л╤И╨╡ ╤Д╨╛╤А╨╝╤Г╨╗╤Л, ╨┐╤А╨╡╨┤╤Б╤В╨░╨▓╨╗╤П╨╡╤В ╤Б╨╛╨▒╨╛╨╣ t-╨╛╤Ж╨╡╨╜╨║╤Г. ╨Ч╨░╤В╨╡╨╝ ╨╖╨╜╨░╤З╨╡╨╜╨╕╨╡ t-╨╛╤Ж╨╡╨╜╨║╨╕ ╨╕ ╤Б╤В╨╡╨┐╨╡╨╜╤М ╤Б╨▓╨╛╨▒╨╛╨┤╤Л ╨╕╤Б╨┐╨╛╨╗╤М╨╖╤Г╤О╤В╤Б╤П ╨┤╨╗╤П ╨╛╨┐╤А╨╡╨┤╨╡╨╗╨╡╨╜╨╕╤П p-╨╖╨╜╨░╤З╨╡╨╜╨╕╤П ╨╕╨╗╨╕ ╨▓╨╡╤А╨╛╤П╤В╨╜╨╛╤Б╤В╨╕ ╤Б ╨╕╤Б╨┐╨╛╨╗╤М╨╖╨╛╨▓╨░╨╜╨╕╨╡╨╝ ╤В╨░╨▒╨╗╨╕╤Ж╤Л T-╤А╨░╤Б╨┐╤А╨╡╨┤╨╡╨╗╨╡╨╜╨╕╤П. ╨в╨░╨║╨╕╨╝ ╨╛╨▒╤А╨░╨╖╨╛╨╝, ╨╛╨┐╤А╨╡╨┤╨╡╨╗╤П╨╡╤В╤Б╤П ╨▓╨╡╤А╨╛╤П╤В╨╜╨╛╤Б╤В╤М ╨┐╨╛╨╗╤Г╤З╨╡╨╜╨╕╤П ╨╢╨╡╨╗╨░╨╡╨╝╨╛╨│╨╛ ╤А╨╡╨╖╤Г╨╗╤М╤В╨░╤В╨░.
╨Т ╨║╨░╤З╨╡╤Б╤В╨▓╨╡ ╨░╨╗╤М╤В╨╡╤А╨╜╨░╤В╨╕╨▓╤Л ╨┤╨╗╤П ╨┐╨╛╨╗╤Г╤З╨╡╨╜╨╕╤П ╤А╨╡╨╖╤Г╨╗╤М╤В╨░╤В╨╛╨▓ ╨╝╨╛╨╢╨╜╨╛ ╨╕╤Б╨┐╨╛╨╗╤М╨╖╨╛╨▓╨░╤В╤М ╨║╨░╨╗╤М╨║╤Г╨╗╤П╤В╨╛╤А╤Л ╨в-╤А╨░╤Б╨┐╤А╨╡╨┤╨╡╨╗╨╡╨╜╨╕╤П ╨╕╨╖ ╨Ш╨╜╤В╨╡╤А╨╜╨╡╤В╨░.
╨Я╤А╨╕╨╝╨╡╤А
ABC Poultry Farms ╨┐╨╛╤Б╤В╨░╨▓╨╗╤П╨╡╤В ╤П╨╣╤Ж╨░. ╨Ъ╨╛╨╝╨┐╨░╨╜╨╕╤П ╤Г╤В╨▓╨╡╤А╨╢╨┤╨░╨╡╤В, ╤З╤В╨╛ ╨╡╨╡ ╤П╨╣╤Ж╨░ ╨╛╤Б╤В╨░╤О╤В╤Б╤П ╤Б╨▓╨╡╨╢╨╕╨╝╨╕ ╨▓ ╤В╨╡╤З╨╡╨╜╨╕╨╡ ╨┐╤П╤В╨╕ ╨┤╨╜╨╡╨╣ ╨┐╤А╨╕ ╤Е╤А╨░╨╜╨╡╨╜╨╕╨╕ ╨▓ ╤Е╨╛╨╗╨╛╨┤╨╕╨╗╤М╨╜╨╕╨║╨╡. ╨Р╨╜╨░╨╗╨╕╤В╨╕╨║ ╨╛╤В╨▒╨╕╤А╨░╨╡╤В 25 ╤П╨╕╤Ж, ╤З╤В╨╛╨▒╤Л ╨┐╤А╨╛╨▓╨╡╤А╨╕╤В╤М ╤Н╤В╨╛ ╤Г╤В╨▓╨╡╤А╨╢╨┤╨╡╨╜╨╕╨╡. ╨б╤А╨╡╨┤╨╜╤П╤П ╤Б╨▓╨╡╨╢╨╡╤Б╤В╤М ╤П╨╕╤Ж ╤Б╨╛╤Б╤В╨░╨▓╨╕╨╗╨░ 4,5 ╨┤╨╜╤П ╨┐╤А╨╕ ╤Б╤В╨░╨╜╨┤╨░╤А╤В╨╜╨╛╨╝ ╨╛╤В╨║╨╗╨╛╨╜╨╡╨╜╨╕╨╕ ╨▓ ╤Б╤Г╤В╨║╨╕. ╨Х╤Б╨╗╨╕ ╤Г╤В╨▓╨╡╤А╨╢╨┤╨╡╨╜╨╕╨╡ ╨║╨╛╨╝╨┐╨░╨╜╨╕╨╕ ╨▓╨╡╤А╨╜╨╛, ╨╜╨░╨╣╨┤╨╕╤В╨╡ ╨▓╨╡╤А╨╛╤П╤В╨╜╨╛╤Б╤В╤М ╤В╨╛╨│╨╛, ╤З╤В╨╛ ╨▓╤Б╨╡ ╨╛╤В╨╛╨▒╤А╨░╨╜╨╜╤Л╨╡ ╤П╨╣╤Ж╨░ ╨┐╤А╨╛╨╢╨╕╨▓╤Г╤В ╨╛╨║╨╛╨╗╨╛ 4,5 ╨┤╨╜╨╡╨╣.
╨а╨╡╤И╨╡╨╜╨╕╨╡:
╨Ф╨░╨╜╨╜╤Л╨╣:- ╤Е╠Д = 4,5 ╨┤╨╜╤П
- ╨╝ = 5 ╨┤╨╜╨╡╨╣
- ╤Б = 1 ╨┤╨╡╨╜╤М
- ╨┐ = 25
╨Я╨╛╤Н╤В╨╛╨╝╤Г,
╤В = (x╠Д-┬╡)/(s/тИЪn)╤В = (4,5 тАУ 5)/(1/тИЪ25)
╤В = -0,5/0,2 = -2,5
╨Я╨╛╤Б╨║╨╛╨╗╤М╨║╤Г ╨╖╨╜╨░╨║ ╨╝╨╕╨╜╤Г╤Б ╨╖╨┤╨╡╤Б╤М ╨╜╨╡╤Г╨╝╨╡╤Б╤В╨╡╨╜, ╨┐╨╛╨╗╤Г╤З╨░╨╡╨╝ t = 2,5.
╨б╤В╨╡╨┐╨╡╨╜╤М ╤Б╨▓╨╛╨▒╨╛╨┤╤Л (df) = n тАУ 1
╨┤╤Д = 25 тАУ 1 = 24
╨в╨░╨║╨╕╨╝ ╨╛╨▒╤А╨░╨╖╨╛╨╝, ╤Б╨╛╨│╨╗╨░╤Б╨╜╨╛ t-╨║╤А╨╕╤В╨╡╤А╨╕╤О ╨▓╨╡╤А╨╛╤П╤В╨╜╨╛╤Б╤В╤М (p-╨╖╨╜╨░╤З╨╡╨╜╨╕╨╡) ╤В╨╛╨│╨╛, ╤З╤В╨╛ ╤П╨╣╤Ж╨░ ╨╜╨╡ ╤Б╨╛╤Е╤А╨░╨╜╤П╤В╤Б╤П ╨▒╨╛╨╗╨╡╨╡ 4,5 ╨┤╨╜╨╡╨╣, ╤Б╨╛╤Б╤В╨░╨▓╨╗╤П╨╡╤В 0,01965418.
╨Я╤А╨╕╨╝╨╡╤З╨░╨╜╨╕╨╡. ╨з╤В╨╛╨▒╤Л ╨╜╨░╨╣╤В╨╕ p-╨╖╨╜╨░╤З╨╡╨╜╨╕╨╡, ╨╝╤Л ╨┐╨╛╨┤╤Б╤В╨░╨▓╨╕╨╗╨╕ ╨╖╨╜╨░╤З╨╡╨╜╨╕╤П t-╨┐╨╛╨║╨░╨╖╨░╤В╨╡╨╗╤П ╨╕ ╤Б╤В╨╡╨┐╨╡╨╜╨╕ ╤Б╨▓╨╛╨▒╨╛╨┤╤Л ╨▓ ╨╛╨╜╨╗╨░╨╣╨╜-╨║╨░╨╗╤М╨║╤Г╨╗╤П╤В╨╛╤А, ╤З╤В╨╛╨▒╤Л ╨┐╨╛╨╗╤Г╤З╨╕╤В╤М ╤А╨╡╨╖╤Г╨╗╤М╤В╨░╤В: 0,01965418.
╨в-╤А╨░╤Б╨┐╤А╨╡╨┤╨╡╨╗╨╡╨╜╨╕╨╡ ╨┐╤А╨╛╤В╨╕╨▓ ╨╜╨╛╤А╨╝╨░╨╗╤М╨╜╨╛╨│╨╛ ╤А╨░╤Б╨┐╤А╨╡╨┤╨╡╨╗╨╡╨╜╨╕╤П
╨Ю╨╜╨╛ ╨╛╤В╨╗╨╕╤З╨░╨╡╤В╤Б╤П ╨╛╤В ╨╜╨╛╤А╨╝╨░╨╗╤М╨╜╨╛╨│╨╛ ╤А╨░╤Б╨┐╤А╨╡╨┤╨╡╨╗╨╡╨╜╨╕╤П, ╨╜╨╛ ╨╛╨▒╨░ ╨╛╨▒╤А╨░╨╖╤Г╤О╤В ╤Б╨╕╨╝╨╝╨╡╤В╤А╨╕╤З╨╜╤Г╤О ╨║╨╛╨╗╨╛╨║╨╛╨╗╨╛╨╛╨▒╤А╨░╨╖╨╜╤Г╤О ╨║╤А╨╕╨▓╤Г╤О. ╨Ъ╤А╨╛╨╝╨╡ ╤В╨╛╨│╨╛, ╨╛╨▒╨░ ╨┐╤А╨╕╨▓╨╛╨┤╤П╤В ╨║ ╤Б╤А╨╡╨┤╨╜╨╡╨╝╤Г ╨╖╨╜╨░╤З╨╡╨╜╨╕╤О, ╤А╨░╨▓╨╜╨╛╨╝╤Г ╨╜╤Г╨╗╤О. ╨Х╤Б╨╗╨╕ ╤Б╤В╨╡╨┐╨╡╨╜╤М ╤Б╨▓╨╛╨▒╨╛╨┤╤Л ╨▓╤Л╤Б╨╛╨║╨░, ╤В╨╛ ╨┐╨╛╨╗╤Г╤З╨╡╨╜╨╜╨╛╨╡ ╨╖╨╜╨░╤З╨╡╨╜╨╕╨╡ ╨в-╤А╨░╤Б╨┐╤А╨╡╨┤╨╡╨╗╨╡╨╜╨╕╤П ╤Б╤В╤Г╨┤╨╡╨╜╤В╨╛╨▓ ╨┐╤А╨╕╨▒╨╗╨╕╨╢╨░╨╡╤В╤Б╤П ╨║ ╨╖╨╜╨░╤З╨╡╨╜╨╕╤О ╨╜╨╛╤А╨╝╨░╨╗╤М╨╜╨╛╨│╨╛ ╤А╨░╤Б╨┐╤А╨╡╨┤╨╡╨╗╨╡╨╜╨╕╤П.
╨а╨░╨╖╨╗╨╕╤З╨╕╤П ╨╖╨░╨║╨╗╤О╤З╨░╤О╤В╤Б╤П ╨▓ ╤Б╨╗╨╡╨┤╤Г╤О╤Й╨╡╨╝:
╨Ю╤Б╨╜╨╛╨▓╨░╨в-╤А╨░╤Б╨┐╤А╨╡╨┤╨╡╨╗╨╡╨╜╨╕╨╡╨Э╨╛╤А╨╝╨░╨╗╤М╨╜╨╛╨╡ ╤А╨░╤Б╨┐╤А╨╡╨┤╨╡╨╗╨╡╨╜╨╕╨╡MeaningIt тАФ ╤Н╤В╨╛ ╨╜╨╡╨┐╤А╨╡╤А╤Л╨▓╨╜╨░╤П ╨▓╨╡╤А╨╛╤П╤В╨╜╨╛╤Б╤В╨╜╨░╤П ╨╝╨╡╤А╨░, ╨▓ ╨║╨╛╤В╨╛╤А╨╛╨╣ t-╨╛╤Ж╨╡╨╜╨║╨░ ╨╕ ╤Б╤В╨╡╨┐╨╡╨╜╤М ╤Б╨▓╨╛╨▒╨╛╨┤╤Л ╨╛╨▒╨╡╤Б╨┐╨╡╤З╨╕╨▓╨░╤О╤В p-╨╖╨╜╨░╤З╨╡╨╜╨╕╨╡ ╨╜╨░╨▒╨╛╤А╨░ ╨┤╨░╨╜╨╜╤Л╤Е. ╨Ю╨╜ ╨╕╤Б╨┐╨╛╨╗╤М╨╖╤Г╨╡╤В╤Б╤П ╨┐╤А╨╕ ╨╜╨╡╨▒╨╛╨╗╤М╤И╨╛╨╝ ╤А╨░╨╖╨╝╨╡╤А╨╡ ╨▓╤Л╨▒╨╛╤А╨║╨╕ ╨╕ ╨╛╤В╤Б╤Г╤В╤Б╤В╨▓╨╕╨╕ ╨╕╨╜╤Д╨╛╤А╨╝╨░╤Ж╨╕╨╕ ╨╛ ╤Б╤В╨░╨╜╨┤╨░╤А╤В╨╜╨╛╨╝ ╨╛╤В╨║╨╗╨╛╨╜╨╡╨╜╨╕╨╕ ╨│╨╡╨╜╨╡╤А╨░╨╗╤М╨╜╨╛╨╣ ╤Б╨╛╨▓╨╛╨║╤Г╨┐╨╜╨╛╤Б╤В╨╕. ╨Э╨╛╤А╨╝╨░╨╗╤М╨╜╨╛╨╡ ╤А╨░╤Б╨┐╤А╨╡╨┤╨╡╨╗╨╡╨╜╨╕╨╡ ╤П╨▓╨╗╤П╨╡╤В╤Б╤П ╨╜╨░╨╕╨▒╨╛╨╗╨╡╨╡ ╤А╨░╤Б╨┐╤А╨╛╤Б╤В╤А╨░╨╜╨╡╨╜╨╜╤Л╨╝ ╨╜╨╡╨┐╤А╨╡╤А╤Л╨▓╨╜╤Л╨╝ ╤А╨░╤Б╨┐╤А╨╡╨┤╨╡╨╗╨╡╨╜╨╕╨╡╨╝ ╨▓╨╡╤А╨╛╤П╤В╨╜╨╛╤Б╤В╨╡╨╣. ╨Ю╨╜ ╨╕╤Б╨┐╨╛╨╗╤М╨╖╤Г╨╡╤В╤Б╤П ╨┤╨╗╤П ╨┐╤А╨╛╨▓╨╡╤А╨║╨╕ ╤Б╨╗╤Г╤З╨░╨╣╨╜╤Л╤Е ╨╜╨╡╨╖╨░╨▓╨╕╤Б╨╕╨╝╤Л╤Е ╨▓╨╡╨╗╨╕╤З╨╕╨╜. ╨╛╤В╨║╨╗╨╛╨╜╨╡╨╜╨╕╨╡ ╨╕╨╖╨▓╨╡╤Б╤В╨╜╨╛. ╨Ъ╤А╨╕╨▓╨░╤П╨в-╨║╤А╨╕╨▓╨░╤П ╨▒╨╛╨╗╨╡╨╡ ╨┐╨╗╨╛╤Б╨║╨░╤П ╨╕ ╤В╤П╨╢╨╡╨╗╨░╤П ╨╜╨░ ╤Е╨▓╨╛╤Б╤В╨░╤Е. ╨б╤В╨░╨╜╨┤╨░╤А╤В╨╜╨░╤П ╨║╤А╨╕╨▓╨░╤П ╨╜╨╛╤А╨╝╨░╨╗╤М╨╜╨╛╨│╨╛ ╤А╨░╤Б╨┐╤А╨╡╨┤╨╡╨╗╨╡╨╜╨╕╤П ╨┤╨╗╨╕╨╜╨╜╨╡╨╡ ╨╕ ╤В╨╛╨╜╤М╤И╨╡ ╨╜╨░ ╤Е╨▓╨╛╤Б╤В╨░╤Е.
╨Ч╨┤╨╡╤Б╤М x╠Д тАФ ╨▓╤Л╨▒╨╛╤А╨╛╤З╨╜╨╛╨╡ ╤Б╤А╨╡╨┤╨╜╨╡╨╡; ╬╝ тАФ ╤Б╤А╨╡╨┤╨╜╨╡╨╡ ╨╖╨╜╨░╤З╨╡╨╜╨╕╨╡ ╨│╨╡╨╜╨╡╤А╨░╨╗╤М╨╜╨╛╨╣ ╤Б╨╛╨▓╨╛╨║╤Г╨┐╨╜╨╛╤Б╤В╨╕; s тАФ ╤Б╤В╨░╨╜╨┤╨░╤А╤В╨╜╨╛╨╡ ╨╛╤В╨║╨╗╨╛╨╜╨╡╨╜╨╕╨╡; n — ╤А╨░╨╖╨╝╨╡╤А ╨▓╤Л╨▒╨╛╤А╨║╨╕. Z = (X — ┬╡)/╧Г’
╨Ч╨┤╨╡╤Б╤М Z тАФ Z-╨╛╤Ж╨╡╨╜╨║╨░ ╨╜╨░╨▒╨╗╤О╨┤╨╡╨╜╨╕╨╣; ┬╡ ╨╛╨╖╨╜╨░╤З╨░╨╡╤В ╤Б╤А╨╡╨┤╨╜╨╡╨╡ ╨╖╨╜╨░╤З╨╡╨╜╨╕╨╡ ╨╜╨░╨▒╨╗╤О╨┤╨╡╨╜╨╕╨╣, ╨░ ╧Г тАУ ╤Б╤В╨░╨╜╨┤╨░╤А╤В╨╜╨╛╨╡ ╨╛╤В╨║╨╗╨╛╨╜╨╡╨╜╨╕╨╡.
╨з╨░╤Б╤В╨╛ ╨╖╨░╨┤╨░╨▓╨░╨╡╨╝╤Л╨╡ ╨▓╨╛╨┐╤А╨╛╤Б╤Л (FAQ)
1. ╨Ъ╨░╨║╨╛╨▓╤Л ╤Б╨▓╨╛╨╣╤Б╤В╨▓╨░ T-Distribution?
╨Э╨╕╨╢╨╡ ╨┐╤А╨╕╨▓╨╡╨┤╨╡╨╜╤Л ╤А╨░╨╖╨╗╨╕╤З╨╜╤Л╨╡ ╤Б╨▓╨╛╨╣╤Б╤В╨▓╨░:
тАв ╨б╨╕╨╝╨╝╨╡╤В╤А╨╕╤З╨╜╨░╤П ╨║╨╛╨╗╨╛╨║╨╛╨╗╨╛╨╛╨▒╤А╨░╨╖╨╜╨░╤П ╨║╤А╨╕╨▓╨░╤П ╤Б ╨▒╨╛╨╗╨╡╨╡ ╤В╨╛╨╗╤Б╤В╤Л╨╝╨╕ ╤Е╨▓╨╛╤Б╤В╨░╨╝╨╕;
тАв ╤Е╨а╨╡╨║╨╛╨╝╨╡╨╜╨┤╤Г╨╡╨╝╤Л╨╡ ╤Б╤В╨░╤В╤М╨╕
╨н╤В╨░ ╤Б╤В╨░╤В╤М╤П ╨┐╤А╨╡╨┤╤Б╤В╨░╨▓╨╗╤П╨╡╤В ╤Б╨╛╨▒╨╛╨╣ ╤А╤Г╨║╨╛╨▓╨╛╨┤╤Б╤В╨▓╨╛ ╨┐╨╛ ╤В╨╛╨╝╤Г, ╤З╤В╨╛ ╤В╨░╨║╨╛╨╡ T-Distribution. ╨Ь╤Л ╨╛╨▒╤К╤П╤Б╨╜╤П╨╡╨╝ ╨╡╨│╨╛ ╨╕╤Б╨┐╨╛╨╗╤М╨╖╨╛╨▓╨░╨╜╨╕╨╡ ╨▓ ╤Б╤В╨░╤В╨╕╤Б╤В╨╕╨║╨╡, ╤А╨░╤Б╤З╨╡╤В, ╨┐╤А╨╕╨╝╨╡╤А ╨╕ ╨╛╤В╨╗╨╕╤З╨╕╤П ╨╛╤В ╨╜╨╛╤А╨╝╨░╨╗╤М╨╜╨╛╨│╨╛ ╤А╨░╤Б╨┐╤А╨╡╨┤╨╡╨╗╨╡╨╜╨╕╤П. ╨Я╨╛╨┤╤А╨╛╨▒╨╜╨╡╨╡ ╨╛╨▒ ╤Н╤В╨╛╨╝ ╨▓╤Л ╨╝╨╛╨╢╨╡╤В╨╡ ╤Г╨╖╨╜╨░╤В╤М ╨╕╨╖ ╤Б╨╗╨╡╨┤╤Г╤О╤Й╨╕╤Е ╤Б╤В╨░╤В╨╡╨╣ тАФ
- ╨Т╤Л╨▓╨╡╨┤╨╡╨╜╨╜╤Л╨╣ ╤Б╤В╨░╤В╨╕╤Б╤В╨╕╨║╨░
- ╨д╨╛╤А╨╝╤Г╨╗╨░ ╤А╨░╤Б╨┐╤А╨╡╨┤╨╡╨╗╨╡╨╜╨╕╤П T
- ╨Т╤Л╨▒╨╛╤А╨╛╤З╨╜╨╛╨╡ ╤А╨░╤Б╨┐╤А╨╡╨┤╨╡╨╗╨╡╨╜╨╕╨╡
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