In: Statistics and Probability
Describe a scenario where a researcher could use an F-test for the equality of two variances to answer a research question. Fully describe the scenario and the variables involved and explain the rationale for your answer. Why is that test appropriate to use?
Let us consider a scenario of production of soft drinks of two different brands. Researchers wants to check whether the amount of soft drinks in the bottles of 250 ml of these two brands have an equal variability or not. For checking this claim, researchers collect the random sample of 10 bottles of soft drinks from brand A and another random sample of 10 bottles of soft drinks from brand B. Then researcher calculates the standard deviations for the amount of soft drinks for the both samples. It was assumed that the samples are from normally distribution population. The amount of soft drinks in the bottle of 250 ml follows an approximate normal distribution with mean 250 ml with known population standard deviation. In this case, a researcher needs to use the F test for the equality of two variances to answer a research question. This test is appropriate because all assumptions of normality and independent samples are satisfied. The independent variable for this research is type of brand and dependent variable is amount of soft drink in the bottle of 250 ml. By using F test for equality of population variances, researcher can check the claim about research study.