Business Research Methods Study Set 5

Business

Quiz 17 :
Hypothesis Testing

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Quiz 17 :
Hypothesis Testing

Hypothesis testing is performed to determine the behavior of the population data by performing the appropriate statistical test on the sample data derived from population a. The selection of appropriate statistical test depends on the number of sample sizes, type of measurement scale and also whether individual case is independent or related. The statistical tests are classified into parametric and non-parametric. The difference between these two is that the parametric tests have more assumptions to be met unlike non parametric test. The population data in the parametric test is normally distributed but the population data is distribution free in the non-parametric test. Parametric test handles the interval and ratio data and non-parametric test handles nominal and ordinal data b. When a hypothesis test is performed, there is possible to occur two types of errors i.e. Type I and Type II. The difference between these two errors is that type I error occurs when null hypothesis is rejected even if it is true and the type II error occurs if null hypothesis is not rejected when it is false. The risk of type I error can be lowered by using the lower alpha value. The type II error is majorly depends on the power of the test performed. So, the risk of type II error can be lowered by choosing the powerful test, which is possible for large sample size. c. Hypothesis is defined in the beginning of the classical test of significance. Hypothesis is defined in two ways i.e. null hypothesis and alternative hypothesis. The statement of the null hypothesis defines that there is no significance difference between two variables and the statement of the alternative hypothesis is that there is significance difference between two variables. The difference between these two hypotheses is that the statement of the null hypothesis is logically opposite to the statement of the alternative hypothesis. Mostly researcher tries to prove the statement of alternative hypothesis by rejecting the null hypothesis. d. The sample data collected for the hypothesis test is used to compute the test statistic. The test statistic value can fall in two regions i.e. region of acceptance and region of rejection. The difference between the these two regions is that when the statistic falls in a specified range, which allows to accept the null hypothesis is called region of acceptance and when the statistic falls in a range, which allows to reject the null hypothesis, is called region of rejection. e. The region of rejection of the hypothesis can be either one tail or two tail test. The difference between these two is that if the rejection region is on one side of the sampling distribution then it is one tail test but if the rejection region is on both side of the sampling distribution then it is two tail tests. For example: if the alternative hypothesis states that mean value is greater than 6, then it is one tail test. If the alternative hypothesis states that mean value can be either greater or less than 6, then rejection region consists numbers greater than 6 and also less than 6.

Hypothesis testing is performed to determine the behavior of the population data by performing the appropriate statistical test on the sample data derived from population. Hypothesis testing is a six step procedure. The summary of these steps is as follows: • Construct the null hypothesis and alternative hypothesis based on the problem statement. Null hypothesis states that there exists no difference and alternative hypothesis states that there exists difference. • Select the appropriate statistical test (i.e. parametric or non-parametric tests) based on the assumptions, size of data and measurement. • Determine the level of confidence i.e. alpha value. The most frequently used level of confidence is 0.5 • Further, obtain the calculated value by doing necessary calculations and computations using the formula. • Further, obtain the critical value or table value (i.e. p- value) by referring to the appropriate table. • Finally, make the conclusion whether to reject null hypothesis or alternative hypothesis. In general, if the calculated value is greater than p-value, then null hypothesis is rejected. The virtue of the hypothesis testing procedure is useful to decide the accuracy of hypothesis because the assumptions are based on population and the test is performed on sample data.

Anova, which is also known as analysis of variance, is the method used to find the difference between the means of two or three groups in the sample. In Anova, every group has its own mean, where the values in that group deviate from that mean. Grand mean is generated by all the data points of sample i.e. from all of the groups. Total variation is calculated by the sum of the squared difference between grand mean and each data point. The total variation is divided into mean square between and mean square within. The mean square within is the variance in the population (i.e. overall), and mean square between is the variance in each group. The purpose of mean square of within ad mean square between is to calculate the F- statistic which determines whether the mean values of each group are significant or not. F - Statistic is calculated by dividing mean square between and mean square within. The acceptance or rejection of null hypothesis is based on the F- value and significance level. If the null hypothesis is accepted, then it is concluded that there is no significance difference between population means. Thus, F- ratio value would be close to 1.