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Здравствуйте! Прошу помощи в следующем вопросе: 1. В таблице приведены сгруппированные данные о коэффициентах соотношения заемных и собственных средств на 100 малых предприятиях региона. Номер интервала Интервал Середина интервала x_i n_i 1 5,05-5,15 5,1 5 2 5,15-5,25 5,2 8 3 5,25-5,35 5,3 12 4 5,35-5,45 5,4 20 5 5,45-5,55 5,5 26 6 5,55-5,65 5,6 15 7 5,65-5,75 5,7 10 8 5,75-5,85 5,8 4
Построить доверительные интервалы для среднего и для следующего наблюдения с надежностью 95%, используя нормальное приближение. 2. В селе Петрово проведено выборочное обследование доходов жителей. По выборке из 25 человек получено среднее 2380 руб. и среднее квадратическое отклонение 90 руб. Можно ли утверждать на уровне значимости 5%, что средний доход жителей составляет менее 2500 руб.? 3. В городах Усатово и Полосатово проведены выборочные обследования доходов жителей. По выборкам из 100 человек получены следующие результаты: в Усатово – средний доход 4050 руб., среднее квадратическое отклонение 105 руб.; в Полосатово – средний доход 3970, среднее квадратическое отклонение 85 руб. Можно ли утверждать на уровне значимости 5%, что в Усатово живут в среднем так же, как и в Полосатово?
Анна Витальевна! Предлагаю Вам впредь не рассматривать несколько не связанных между собой задач в рамках одной консультации. Не удивляйтесь, если получите консультацию только по одной задаче. Прочитайте правила портала.
а) Насколько я понимаю, задача решается через доверительные интервалы. б) Насколько я помню, для доверительных интервалов требуется знание о законе распределении вероятности. в) Лично мне пока известны доверительные интервалы только для нормального распределения.
Можно ли утверждать, что доходы жителей села распределены по нормальному закону или это принципиально неизвестно?
В условии задачи 1 ведь написано: "Построить доверительные интервалы для среднего и для следующего наблюдения с надежностью 95%, используя нормальное приближение". В задачах 2 и 3 нужно найти доверительные интервалы для доходов жителей. Доходы рассматриваются как случайные величины. Прочитайте Доверительный интервал.
Проверьте пожалуйста 2 задачу: Итак, дано: x ̅=2380; σ=90,n=25,α=0,05 По таблице Стьюдента найдем t по уровню значимости и числу степеней свободы t(0,05;k-1)=t(0,05;25-1)=t(0,05;24)=2,06 Найдем средний доход жителей: x ̅-t*σ/√n<X ̅<x ̅+t*σ/√n 2380-2,06*90/√25<X ̅<2380+2,06*90/√25 2342,92<X ̅<2417,08
Извините, но я не брался Вас консультировать непосредственно. Поэтому проверять решение задачи не стану. Буду рад, если Вам помогли мои советы как модератора. Можете считать их "советами прохожего". Главное, чтобы они Вам не навредили...
Я ещё раз предлагаю Вам не рассматривать в рамках одной консультации несколько задач. То Вы понимаете, как решаются вторая и третья задачи, то не понимаете... То обсуждаете первую задачу, то снова возвращаетесь к другим... Нехорошо как-то!
Ведь я же вам говорил, что для доверительных интервалов требуется знание о законе распределении вероятности, и что существуют доверительные интервалы для нормального распределения. Вы взяли именно эту формулу. Т.е. предложенное вами решение обязательно требует, чтобы доход жителей был случайной величиной, имеющй нормальное распределение вероятностей. О чём, собственно, я вас ранее и спрашивал.
Если же брать тот ответ, который вы мне дали -- "Это неизвестно" -- то задача не имеет решения.
Форма ответа
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