Question

Question 3) A convenience store chain wants to determine the relationship between the income of customers and the frequency of visiting stores in the chain. To answer your client’s question, you would do a test of hypothesis. State the null and alternative hypotheses for this particular study. Which significance level alpha would you select? If both income and “frequency of store visits” were measured on ordinal scales, how would you analyze the relationship between these two variables? Set up an example to illustrate your answer in the case of ordinal-scale variables and explain what kind of result would be evidence of this hypothetical relationship.

Answer 1

The relationship between the two variables is measured by Correlation coefficient.

For this,we will do t-test for testing the significance of an observed sample correlation coefficient. Now if r is the observed correlation coefficient in a sample of n pair of observations between the income of the customers and the frequency of visiting stores, then the null hypothesis, H0:p=0,that is, the population correlation coefficient is 0, the statistic

t= [r/sqrt(1- r^2)]*sqrt(n-2) follows t-distribution with (n-2)d.f.

For ordinal set of data ,we will calculate Spearman's correlation coefficient based on the ranks for the sample,then hypothesis for t-test is applied.If the test concludes that the correlation coefficient is significantly different from 0,we say that the correlation coefficient is significant..