The purpose of any statistical calculations is creation of probabilistic model of any given casual event. It allows to collect and analyze data on concrete observations or experiments. The confidential interval is used at small sample that allows to define high degree of reliability.
It is required to you
- - table of values of function of Laplace.
Instruction
1. The confidential interval of probability theory serves for assessment of expected value. In relation to the concrete parameter analyzed by statistical methods it is such interval which blocks value of this size with the set accuracy (degree or level of reliability).
2. Let the random variable x be distributed under the normal law and the mean square deviation is known. Then the confidential interval is equal: m(x) – t · σ/√ n
Laplace's function is used in the given formula to determine the probability of hit of value of parameter in this interval. As a rule, at the solution of similar tasks it is required or to calculate function through an argument, or on the contrary. The formula for finding of function represents quite bulky integral therefore for simplification of work with probabilistic models use the ready table of values.
Example: To find a confidential interval with the level of reliability 0.9 for the estimated sign of a certain population x if it is known that the mean square deviation σ is equal 5, a selective average of m (x) = 20, n volume = 100.
Decision: Define what sizes participating in a formula are unknown to you. In this case this expected value and Laplace's argument.
On a statement of the problem the value of function is equal 0.9, therefore, define t from the table: Φ(t) = 0.9 → t = 1.65.
Substitute all known data in a formula and calculate confidential limits: 20 – 1.65·5/10
3. Laplace's function is used in the given formula to determine the probability of hit of value of parameter in this interval. As a rule, at the solution of similar tasks it is required or to calculate function through an argument, or on the contrary. The formula for finding of function represents quite bulky integral therefore for simplification of work with probabilistic models use the ready table of values.
4. Example: To find a confidential interval with the level of reliability 0.9 for the estimated sign of a certain population x if it is known that the mean square deviation σ is equal 5, a selective average of m (x) = 20, n volume = 100.
5. Decision: Define what sizes participating in a formula are unknown to you. In this case this expected value and Laplace's argument.
6. On a statement of the problem the value of function is equal 0.9, therefore, define t from the table: Φ(t) = 0.9 → t = 1.65.
7. Substitute all known data in a formula and calculate confidential limits: 20 – 1.65·5/10