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РАСЧЕТНО-ГРАФИЧЕСКАЯ РАБОТА. Labra1111ГОТОВО. Первичная обработка статистических данных


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АнкорРАСЧЕТНО-ГРАФИЧЕСКАЯ РАБОТА
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5. Доверительные интервалы для неизвестных математического ожидания и дисперсии


Если не известны математическое ожидание и дисперсия, то доверительный интервал для математического ожидания m рассчитывается по следующей формуле

.

Здесь , рассчитанные ранее точечные оценки, – объем выборки, – квантиль распределения Стьюдента, который определяется по таблицам, – было рассчитано в предыдущем пункте.

При больших степенях свободы ( ) распределение Стьюдента стремится к нормальному закону, при этом условии квантиль можно смотреть по таблице нормального распределения.

.

(Все это подставляем в формулу

,

.

Таким образом, математическое ожидание с вероятностью 90% принадлежит интервалу .

Доверительный интервал для дисперсии вычисляется по следующей формуле

.

Значение при больших степенях свободы приближенно можно вычислить по следующей формуле .

Таким образом, в нашем случае





Следует заметить, что , поэтому , а квантиль был найден ранее по таблице.

Подставляя полученные результаты в формулу для вычисления доверительного интервала, получим

,

.

Следовательно, с вероятностью 90% дисперсия генеральной совокупности принадлежит интервалу .

Данные к лабораторной работе

№ вар

Выборка



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