Abstract

Mathematical statistics is a science that develops mathematical methods and systematic use of statistics for scientific and practical conclusions.

In many of his areas of mathematical statistics is based on probability theory to gauge the reliability and accuracy of the findings made on the basis of limited statistical data (eg, to estimate the required sample size to produce the results desired accuracy in a sample survey).

Allocate descriptive statistics, theory of estimation and hypothesis testing theory. Descriptive statistics is a set of empirical methods used for the visualization and interpretation of data (calculation of sample characteristics, tables, charts, graphs, etc.) usually do not require assumptions about the probabilistic nature of the data.

Some methods involve the use of descriptive statistics capabilities of modern computers. These include, in particular, cluster analysis, aimed at the selection of groups of objects, similar to each other, and multidimensional scaling, which allows to visualize the objects in the plane.

Calculations

I. Make assumptions. Here we must describe all necessary assumptions for our test, which we will provide later.

II. Stating hypothesizes. In this stage we have to state the null and alternative hypothesizes and select a probability of type 1 error (alpha level)

III. Performing test. Here we must define a distribution of the sample and specify the proper test statistic value.

IV. Calculate the test statistic

V. Conclusions. Compare the obtained statistic value to a criteria value to make a decision and interpret the results.

According to the Standard Normal Table:

- (a) Z score cutoff is 1.645, (b) z-critical =2 (c) we have to reject the null hypothesis

- (a) 1.96, (b) 2, (c) reject

- 2.3263, z=2, we have no enough evidence to reject the null hypothesis

- 2,576, z=2, we have no enough evidence to reject the null hypothesis.

18.

H0: Music has no effect on math problem solving skills. Ha: Music increases the math problem solving skills.

Z=x-ms=58-3510=2.3

The critical value for this test (according to a Standard Normal Table) is 2.3263

Hence, as 2.3<2.3263, we are failing to reject the null hypothesis.