Lecture 39 is continuation of previous lecture on hypothesis testing. In this lecture, we will learn about various types of hypothesis testing, such as test of means, variances and proportions paired comparison hypothesis testing often in hypothesis testing, the sample measures are tested against the population measures. How will we test by using both the measures and finding our tests Statistics define a confidence level of test identify the rejection regions using the confidence level compare whether the test statistic fall in the rejection region or not. That is have an illustration of this we have collected a sample from a population. Now, we have two measures the sample mean x bar and population mean new. Now we test whether there is any significant difference between sample mean and file population mean, but how do we test first of all, we define a test statistic by using both the measures of population and sample such as population mean mu and sample mean x bar then we check whether this test statistic fall in the acceptance region or not.

The acceptance region is nothing but the area below curve corresponding to the confidence level of testing. Now, it is not mandatory that we check Means of sample and populations. We can also check other measures such as variants or proportions. Based on the measures we use to test the hypothesis, we can categorize hypothesis tests, test off means test off variances and test off proportions. The test of means include z test and T test based on normal and T distributions, respectively. Similarly, the test of variance could be among F tests and chi square test.

Do you remember the terms? We had discussed these terms in measure face lectures on probability distributions. Finally, the test of proportions could be the test of proportions or T test of proportions. Let us consider examples to understand these tests. Consider a pizza delivery process with known mean delivery time as 30 minutes. What is this?

This is nothing but the population mean. Now, a random sample of 81 deliveries work To obtain mean delivery time as 29.8 minutes. Now, this is sample mean the owner of the shop would like to know whether the sample delivery means significantly differ from the population mean. Now, which type of test Shall we use? Yes. Since, we are going to compare the means, we use any one of the tests for mean let us define the null hypothesis H zero as mew is equals true Muse zero.

The test statistics equation for P is as you see on the screen Let us put the given values in this equation we get the test statistics z zero as minus 0.4. Now, this test statistics is compared with Z value corresponding to the confidence level of testing to decide on whether to accept or reject the null hypothesis for understanding the test of variance. Let us consider the same example, this time with different purpose the pizza delivery process As a known variance of 0.5 minutes what does this indicate? It indicates that the population variance sigma square is equal to 0.5 minutes. Now, from the sample, the owner got a sample variance of 0.25. The owner would like to check whether sample variance deviates significant significantly from the population variance.

Which type of test Shall we use? Yes, since the measure we are going to test as variants, we use methods for test of variance The null hypothesis is defined as h zero as sigma square is equal to sigma zero square. That is use the chi square distribution here for determining the test statistic. The formulae for chi square is as shown, when we put the known values in the formulae, we get the test statistics as 40. Now, use this test statistics to decide on whether to accept or reject the null hypothesis. Similarly, the example for test of proportions This is similar to test of means, here the measure that we are going to test for significance is the proportion of defectives.

The equation for test statistics is also different, a little we can use z test of proportion here. The equation is as you see on the screen, the known values are plotted in the equation to get the test statistic z zero as minus 1.81. We will use this test statistics to decide on accepting our rejecting the null hypothesis based on the confidence level of test, failed comparison is another useful test. For hypothesis. It is used to compare two population means and situations such as before and after performance differences, comparing between two identical processes, etc. method of paired comparison is similar to T test.

That's all for this lecture. We can move to the next lecture to continue with the concepts of hypothesis testing. some more examples. Thank you