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# VZFEI. Statistics. Examination №2

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**21.02.2008**

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# Description

VZFEI. All-Russian Correspondence Financial and Economic Institute.

The solution of problems of the control work №2 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 19 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. The Department of Education, through studies of the question of how much time per week (in hours) of high school students spend on homework, according to the scheme itself, without repetitions random sample surveyed 200 students. The results are shown in the table:

Search:

a) border, which concluded with a probability of 0.95 times the average homework schoolboy.

b) the probability that the proportion of school children who spend on homework more than 17 hours, is different from the proportion of students in the sample is not more than 5% (in absolute terms).

c) the amount of repetitions the sample in which the same boundaries for the average homework time students can be guaranteed with a probability of 0.9876.

2. According to the task number 1, using the chi-square test of Pearson, at a significance level a = 0,05 to test the hypothesis that the random variable X - homework time - normal distribution. Build on one drawing a histogram of the empirical distribution and the corresponding normal curve.

3. The examination of 100 in the number of upgraded equipment failures per month of A (pcs.) And the degree of modernization of the Y (%). The results are shown in the table:

You need:

1) calculate the average group and build 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 the corresponding regression equation to determine the number of failures of the device, if the degree of modernization is 10%.

# Additional information

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Online tutor in mathematics and physics.

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