Testing of hypothesis is a statistical procedure to test a statistician's claim. To test any assertion made regarding a population parameter, we use a sample of that population and try to test if the assertion made is true or not, statistically. The sample size has to be carefully decided keeping the margin of error in mind. Once the sample size is decided, observations are recoded. These observations are recoded from the sample chosen from the sampling frame. The units which finally make it to the sample are called sampling units.
Testing of hypothesis is a stepwise procedure in which we perform 5 major steps to reach to a conclusion.
Step1:Settiing up of the null and alternative hypothesis. A null hypothesis ,H0, is the hypothesis of no difference and alternative hypothesis is the hypothesis which we are testing for. Based on the alternative hypothesis, we either have a one tailed or a two tailed test.
Step 2:After setting up the null and alternative hypothesis , we then calculate the test statistic using the statistics required for that particular test.(This step varies from test to test )
Step 3: We then see the critical value from the standard tables which sets up the critical region. We can also find the p value instead.
Step 4:With the help of p value , we can now decide whether to reject the null hypothesis or not. If the p value is less than the level of significance, we reject the null hypothesis or we say there is insufficient evidence to reject the null hypothesis.
Step 5:The last step is to give a sensible conclusion based on the test results.
There are several hypothesis tests that are described in the course of statistics. These include, proportion test , which is used when we have test for claim about population proportion on anything. Difference in population proportion test, which is used when we have test for difference in two proportions. One sample Z and t test, which is used when we are checking for claim about the population mean. Z test is used in the cases, where sample size is large and population standard deviation is known. T test is used when the sample size is small and population standard deviation is unknown .When sample size is large , using t or Z doesn’t make a big difference.
A sample size is considered large after 30. Another important test of hypothesis is the independent sample t test and the paired sample t test. Independent sample t test is used in the cases, when we want to see if there is difference in means between two groups. The samples taken for this test are independent of each other. We use pooled variance to conduct the test. On the other hand, we use paired sample t test when the samples are dependent on each other. For example if we want to see the affect of new teaching method adopted by teachers, then we may take same set of students to assess their scores before and after the method is adopted. This way we are using the same sample of students, thus it is the paired t test.
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