Hypothesis Testing by Dr Mahamood Usman Khan Ph D IIT ISM Dhanbad M Phil M Sc AMU Hypothesis Hypothesis A statement about the population or population parameter Example Let us suppose that the bulbs manufactured under some standard manufacturing process have an average life of hours and it is proposed to test a new procedure for manufacturing light bulbs Thus we have two populations of bulbs those manufactured by standard process and those manufactured by the new process In this problem the following three hypotheses may be set up i New process is better than standard process ii New process is inferior to standard process iii There is no difference between the two processes Null Hypothesis and Alternative Hypothesis No difference Null Hypothesis statement iii of the light bulb example There is a difference statement i ii of the light bulb example Types of Errors One Tail VS Two Tailed Test One Tailed and Two Tailed Test Suppose we claim that the average age of a college students in a city is 23 Sample Test Instant View Critical Region Level of Significance It is determined by the researcher Symbolized by Affected by the sample size and the nature of experiment Common levels of significance are 0 05 0 01 0 001 Level of Significance is defined as the probability of rejecting the null hypothesis when the null hypothesis is true RP eject 0 HH 0 When P value It is used to test the hypothesis A p value is a statistical measurement used to validate a hypothesis against observed data i e reject the null hypothesis A p value measures the probability of obtaining the observed results assuming that the null hypothesis is true Consider an observed test statistic t from unknown distribution T Then the p value p is what the prior probability would be of observing a test statistic value at least as extreme as t if null hypothesis H0 were true That is Reject null hypothesis H0 Accept null hypothesis H0 c Determination of P value in Upper Lower and Two tailed test z ZP z Steps involving in Hypothesis Testing State Null and Alternative hypothesis Identify appropriate Test Statistics Select a Level of Significance Calculate the Test Statistics p value Conclusion Take the Decision Types of Test Statistics Large sample test n 30 Z test Normal Approximation Z test means and proportions variables and attributes t test mean One sample two sample and paired sample F test Equality of variances Chi Square Test Hypothetical variance Independent of attributes 2 Exact sample test n 30 t F Chi square tests Normal Assumption ThankYou