Examination №4

№1. Under the scheme self-repetitions random sampling conducted a survey 10% of construction companies in the region in terms of the work performed. The results are shown in the table.

The scope of work, mln. Rub. Less than 56 56-60 60-64 64-68 68-72 Over 72 Total

Organisations September 11 19 30 18 13 100

Search:

a) border, which concluded with a probability of 0.9973 average volume of work performed all construction companies in the region;

b) the probability that the proportion of all construction companies, the scope of work of not less than 60 mln. rub., differs from the proportion of organizations in the sample is not more than 0.05 (in absolute value);

c) the amount of repetitions the sample in which the same boundaries for the average amount of work performed (see. p. a) can be guaranteed with a probability of 0.9876.



№2. According to the task 1 using the criterion 2-Pearson, with a significance level of α = 0,05 to test the hypothesis that the random variable X - the volume of work performed - normal distribution. Build on one drawing a histogram of the empirical distribution and the corresponding normal curve.


№3. Distribution of 100 medium-sized farms in the number of hired workers X (pers.) And their average monthly wage per person Y (thousand. Rub.) Presented in the table below:

Y

X 10-20 20-30 30-40 40-50 50-60 60+ Total

102 October 10

103 15 June 21

104 10 11 8 29

105 8 March 11

106 5 June 11

107 9 May 18 April

Total 5 14 28 14 14 25 100

You need:

1) calculate the average group and build and 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 a significance level α = 0,05 to assess its value and draw a conclusion about the direction of distress and relationships between variables X, and Y;

c) using the appropriate regression equation to estimate the average monthly wage per worker of the farm, which employs 10 salaried workers.


References