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Консультация № 199496
03.11.2020, 11:30
0.00 руб.
0
4
1
Здравствуйте, уважаемые эксперты! Прошу Вашей помощи в решении следующей задачи:
Дано:
γ = 0,99
18.6 30.6 29.4 32.1 23.1 32.5 32.9 27.7 32.5 38.4 27.9 19.6 27.5 31.9 42.9 32.9 33.6 25.8 39.9 48.9
По данным выборки, удовлетворяющей нормальному закону распределения вычислить:
1) выборочное среднее;
2) исправленное выборочное среднее квадратическое отклонение;
3) доверительный интервал для математического ожидания при доверительной вероятности γ;
4) доверительный интервал для среднего квадратического отклонения для того же значения γ.
Спасибо!
Дано:
γ = 0,99
18.6 30.6 29.4 32.1 23.1 32.5 32.9 27.7 32.5 38.4 27.9 19.6 27.5 31.9 42.9 32.9 33.6 25.8 39.9 48.9
По данным выборки, удовлетворяющей нормальному закону распределения вычислить:
1) выборочное среднее;
2) исправленное выборочное среднее квадратическое отклонение;
3) доверительный интервал для математического ожидания при доверительной вероятности γ;
4) доверительный интервал для среднего квадратического отклонения для того же значения γ.
Спасибо!
Обсуждение
07.11.2020, 22:23
общий
это ответ
Здравствуйте, Svet_Vitalievna!
1) Выборочное среднее для небольшой выборки длины n проще всего определить по стандартной формуле:
В данном случае n = 20 и
2) Исправленное выборочное среднее квадратическое отклонение также вычисляется стандартно:
В данном случае
3) Если для выборки длины n с нормальным распределением, параметры которого неизвестны, определены выборочные среднее X[sub]в[/sub] и среднеквадратическое отклонение S[sub]в[/sub], то доверительный интервал для математического ожидания при доверительной вероятности [$947$] определяется как
где t[sub]j[/sub]([$947$],n-1) определяется по таблице квантилей распределения Стьюдента. В данном случае находим t[sub]j[/sub](0.99,19) = 2.539 и доверительный интервал
4) Для той же выборки доверительный интервал для среднего квадратического отклонения определяется как
где [$967$][sup]2[/sup]([$945$],k) определяется по таблице квантилей распределения "хи-квадрат". В данном случае находим
и доверительный интервал
1) Выборочное среднее для небольшой выборки длины n проще всего определить по стандартной формуле:
В данном случае n = 20 и
2) Исправленное выборочное среднее квадратическое отклонение также вычисляется стандартно:
В данном случае
3) Если для выборки длины n с нормальным распределением, параметры которого неизвестны, определены выборочные среднее X[sub]в[/sub] и среднеквадратическое отклонение S[sub]в[/sub], то доверительный интервал для математического ожидания при доверительной вероятности [$947$] определяется как
где t[sub]j[/sub]([$947$],n-1) определяется по таблице квантилей распределения Стьюдента. В данном случае находим t[sub]j[/sub](0.99,19) = 2.539 и доверительный интервал
4) Для той же выборки доверительный интервал для среднего квадратического отклонения определяется как
где [$967$][sup]2[/sup]([$945$],k) определяется по таблице квантилей распределения "хи-квадрат". В данном случае находим
и доверительный интервал
5
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