T Test, z-Test, Chi-Square Test, Statistics Assignment Help

Statistics Assignment Help >> T Test, z-Test, Chi-Square Test Assignment Help

The t-test

The t-test can be said to be the statistical hypotheses test where the test statistic follows the student’s t distribution when the null hypotheses is not supported. It’s most common application is in the test statistic following normal distribution where values of scaling terms of test static’s are known. In case the scaling terms are unknown and are replaced by the estimates which are based on data, then the test statistics under certain conditions does follows a student’s t distribution. The t statistics were introduced in the year 1908 by a chemist name William Seasly Gusset, in Dublin, Ireland. He devised the test as a way for cheaply monitoring the qualities of stouts. The t-test are used in

1. One sample location test for finding out the mean of normally distributed populations as signified in the null hypotheses.

2. A two sample location test of null hypothesis where the means of two normally distributed populations are found equal. These tests are also termed as student’s test.

3. The test for whether the slope of regression line is in significant difference from zero.

The z-test

A statistical test for which the distribution of the statistic of the test, which is under the null hypotheses, can be approximated by using a normal distribution and is termed as z-test. The approximated z tests are mostly performed for larger sample sizes, because as per the central limit theorem, many of the test statistics are approximately normally distributed for only the large samples.

Z-test is used for one sample location tests for comparing the mean of given constant’s sets of measurements. When the observed data X1, ..., An are uncorrelated, contain a common mean μ, and also have the common variance of σ2, sample average X has the mean μ and the variance σ2 / n. for the null hypothesis having the mean value of given population as a given number μ0, X −μ2 can be used as the test-statistic. If X −μ0 is large, the null hypotheses can be rejected.

Z test are applicable in the below given conditions

1. The nuisance parameters must be known or must be estimated with high accuracy as the z tests only focus on single parameters while treating the other unknown parameters having fixed true values.

2. A normal distribution must be followed by the test statistic.

The Chi-Square test

In this type of statistical hypotheses test, the sampling distribution is the chi square distribution when the null hypothesis is true or any in which the null hypotheses is untrue. This means that the sampling distribution can be approximated to a chi-square distribution very closely (to the extent of the desire), by increasing the size of the sample. The Pearson’s chi-square test, linear by motion chi-square test, Yates chi-square test, likelihood chi-square test is some of the examples of chi-square test.

The chi-square distribution can be exact when the distribution of the test statistic is the test where the variance of a given population has a given value, which is based on the sample variance. These tests are uncommon in actual practice as the values of variances to be tested against are very seldom known in the exact manner.

We get a known result when we take the sample of size n of a population having the normal distribution. The test can be determined on the basis of the variances of its population having a pre determined value or not.

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