Course Title: Statistics for planners-II

An Assignment

On

Hypothesis Testing

Submitted By: 090430 Date of Submission: 19.09.2010

Urban and Rural Planning Discipline

Khulna University, Khulna

Preface:

A hypothesis is a statement about a population parameter developed for the purpose of testing. The terms hypothesis testing and testing a hypothesis are used interchangeably. Hypothesis testing starts with a statement, or assumption, about a population parameter. The statistical testing of hypothesis is the most important technique in statistical inference. There is a different type of test statistics for hypothesis testing. Here the discussions of four types of test statistics are given below:

• The chi-square test.

• ANOVA (Analysis of variance).

• The z test or large sample test.

• The t test or small sample test.

Z-Test:

The Z-test is a statistical test used in inference which determines if the difference between a sample mean and the population mean is large enough to be statistically significant, that is, if it is unlikely to have occurred by chance.

The "Z-Test" is used a lot in statistical analysis and business research. Usually when a research or survey is carried out, a sample population is interviewed, and the number of people actually interviewed is much smaller than the actual population of the subjects of the research. The researchers carry out the Z-Test to determine whether the results of the survey can be considered as representative of the entire population or not.

When we can do z-test?

➢ When data points are independent from each other.

➢ Z-test is preferable when sample size is greater than 30. ➢ The distributions should be normal if sample size is low, if however sample size>30 the distribution of the data does not have to be normal ➢ When the variances of the samples are same.

➢ When all individuals are selected at random from the population ➢ When all individuals have equal chance of being selected. ➢ Sample sizes should be as equal as possible but some differences are allowed.

T-Test:

A t-test is any statistical hypothesis test in which the test statistic follows a Student's t distribution if the null hypothesis is supported. It is most commonly applied when the test statistic would follow a normal distribution if the value of a scaling term in the test statistic were known. When the scaling term is unknown and is replaced by an estimate based on the data, the test statistic follows a Student's t distribution.

A statistical test involving means of normal populations with unknown standard deviations; small samples are used, based on a variable t equal to the difference between the mean of the sample and the mean of the population divided by a result obtained by dividing the standard deviation of the sample by the square root of the number of individuals in the sample.

When we can do t-test?

➢ Data sets should be independent from each other except in the case of the paired-sample t-test. ➢ T-test is preferable when sample size is less than 30. ➢ When population standard deviation is unknown.

➢ When the distributions are normal for the equal and unequal variance t-test. ➢ When the variances of the samples are same for the equal variance t-test. ➢ When all individuals are selected at random from the population ➢ When all individuals have equal chance of being selected. ➢ Sample sizes should be as equal as possible but some differences are allowed.

F-Test:

An F-test is any statistical test in which the test statistic has an F-distribution under the null hypothesis. It is most often used when comparing statistical models that have been fit to a data set, in order to identify the model that best fits the population from which the data were sampled. A great variety of hypotheses in applied statistics are tested...