V. Вычисление доверительных интервалов для математического ожидания и дисперсии

1. Так как гипотеза о нормальном распределении случайной величины не противоречит опытным данным, то будем считать (с некоторым риском), что случайная величина распределена нормально, причем математическое ожидание и среднее квадратическое отклонение этого распределения неизвестны.

Доверительный интервал для оценки математического ожидания имеет вид:

По доверительной вероятности и числу степенной свободы

находим (например, В.Е.Гмурман “Руководство к решению задач по теории вероятностей и математической статистике” приложение3)величину

,

а затем точность оценки

.

Итак, получим искомый доверительный интервал, покрывающий неизвестное математическое ожидание с заданной надежностью , т.е. интервал

2. Доверительный интервал для имеет вид:

,

Для и по таблице (см. в учебниках В.И. Ермаков “Сборник задач по высшей математике для экономистов” приложение 3 стр. 520 или приложение 4 В.Е. Гмурман “Руководство к решению задач по теории вероятностей и математической статистике”) находим

Отсюда

Поясним смысл, который имеет заданная надежность . Из 100 выборок 95 определяют такие доверительные интервалы, в которых параметр ( и ) действительно заключен, и только в пяти выборках он может выйти за границы доверительного интервала.

VI. Задача

Решение

2,71 2,63 2,21 2,54 2,24 2,43 2,6 2,58 2,46

2,74 2,62 2,51 2,52 2,7 2,36 2,64 2,51 2,59

2,47 2,35 2,43 2,41 2,63 2,22 2,48 2,25 2,32

2,1 2,42 2,41 2,52 2,42 2,46 2,45 2,4 2,16

2,63 2,41 2,38 2,56 2,41 2,7 2,43 2,32 2,41

2,47 2,41 2,42 2,29 2,67 2,35 2,42 2,3 2,26

2,44 2,58 2,54 2,53 2,2 2,38 2,48 2,38 2,26

2,58 2,31 2,46 2,35 2,44 2,21 2,42 2,54 2,54

2,22 2,49 2,58 2,41 2,56 2,65 2,42 2,69 2,56

2,32 2,55 2,42 2,31 2,59 2,45 2,41 2,45 2,44

2,52 2,38 2,43 2,42 2,52 2,3 2,67 2,48 2,63

2,6

I. Skim the text for general understanding.

A business lunch

If you are traveling abroad on business, your most difficult problem is lunch. Every country has different traditions and you should know some of them. Business lunches are very common in many countries and cultures. Food itself is one of the most visible manifestations of a culture and is something people are proud of and like to share with guests to their country. However, just as the food changes from culture to culture so does the intention and etiquette surrounding the lunch. In some cultures the business lunch is a time for communication and building relationships, in others simply an opportunity to talk about business, known as the "working lunch".

As to its length in the south of Europe a business lunch takes much time. In Italy it takes about three hours. In Greece it is like a late dinner and when it comes everyone thinks of food. So don’t worry if business discussion is slow starting. Business waits.

In France a business lunch is usually long, too. Anything under two hours is classed as a coffee break.

In some countries a business lunch is light; in others it is rather heavy. If you find yourself in Scandinavia you will taste sandwiches and drink milk instead of alcohol. Health is above all. In Russia there are no problems with drinking or smoking.

Business lunch is a very popular type of meeting. It is a time to relax a little outside the office and a time to get to know people personally in a less formal atmosphere, while doing something productive.

If you are called upon to make the reservations for such a meeting, look for a quiet place without distractions.

The business lunch in the United States is usually a short meeting, though there are always exceptions. Some time is spent eating and making small talk before more serious matters are discussed.

Lunch is not a big affair in the UK and many an office worker will happily eat a sandwich at their desk. Business lunches however will take place at a restaurant or pub. The British like to keep personal life and business separate unless a good relationship has formed so discussions may very well be centred on business.

As each culture has its own practices, whatever the language of communication. It is best when visiting a foreign country to wait until your host brings up business rather than initiate it yourself, unless you yourself are hosting the meeting. When you hear something like, “Well, let’s get down to business”, then you know the official meeting has begun.

Business lunch discussions, because they are more relaxed, are usually less formal than in-house meetings. The lunches may speak at random jumping into the discussion when they have something to say rather than being more structured; that is not to say that lunch meetings can’t also be formal.

Business lunches start with small talk. Making pleasant conversation with colleagues sets a positive tone for the rest of the meeting. Follow the small-talk guidelines: talk about weather, sports, the restaurant, or type of food you are eating, and avoid politics, religion, and anything negative.