VZFEI. Statistics. Examination №3.

VZFEI. All-Russian Correspondence Financial and Economic Institute.
The solution of problems of the control work №3 matematichekoy statistics.
E-book (DjVu-file) contains solutions 3-x control work tasks for students VZFEI. Solving problems presented in the form of scanned text, collected in a single document of 17 pages. This document is stored in a format DjVu, which is open in Internet Explorer after installing utility program (plug-in). Link to download and install DjVu-plugin can be found on the company's homepage LIZARDTECH. DjVu-file that contains the conditions of tasks and their detailed solution completely and ready for viewing on your computer and print. All tasks were successfully offset VZFEI teachers.

Topics of problems of control work.
1. Boxes of chocolate are packed automatically. Under the scheme self-random sample was taken of 130 repetitions of the 2,000 packages contained in the party, and provided data about their weight:
Search:
a) border, which concluded with a probability of 0.9901 average weight of packages in the lot.
b) the probability that the proportion of packages whose weight less than 1000, the entire batch is different from the proportion of such packages in the sample by no more than 0.05 (in absolute value).
c) the amount of repetitions the sample in which the same boundaries for the average weight of packaging in the whole batch can be guaranteed with a probability of 0.95
2. According to the task №1, using the chi-square test of Pearson, at a significance level a = 0,05 to test the hypothesis that the random variable X - the weight of packages - normal distribution. Build on one drawing a histogram of the empirical distribution and the corresponding normal curve.
3. Distribution of 50 companies on a monthly advertising costs X (thous. Rub.) And the amount of revenue from sales of Y (mln. Rub.) Presented in the table below:
You need:
1) Calculate the group average and construct empirical regression line.
2) Assuming that between the variables X and Y there is a linear correlation:
a) Find the equation of the regression lines and build their schedules on a drawing with empirical regression lines.
b) Calculate the correlation coefficient at the level of significance of a = 0,05 to assess its value and draw a conclusion about the direction of distress and relationship between variables X and Y.
c) Using appropriate regression equation to estimate the average value of sales during the monthly advertising expenses in the amount of 2.4 thousand. rub.