Question

3) You have been asked to study whether there is a statistical relationship between the region of the country and the categorical number of stores that have experienced at least a 20% return rate of the item you are studying. Sample data concerning these two variables is given in appendix three. At both the 5% and 2% levels of significance, is there evidence of a relationship between the region of the country and the categorical number of stores that have experienced at least a 20% rate of return of the item? Appendix Three: Region Number of Stores One Two Three Four <25 18 21 13 28 [25-50) 11 20 19 24 [50-75) 15 17 22 18 [75-100) 9 7 8 10 ≥100 6 5 6 7

Answer 1

Solution:-

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

H₀: The region of the country and the categorical number of stores that have experienced at least a 20% rate of return of the item are independent.
H_a: The region of the country and the categorical number of stores that have experienced at least a 20% rate of return of the item are not independent.

Formulate an analysis plan. For this analysis, the significance level is 0.05. Using sample data, we will conduct a chi-square test for independence.

Analyze sample data. Applying the chi-square test for independence to sample data, we compute the degrees of freedom, the expected frequency counts, and the chi-square test statistic. Based on the chi-square statistic and the degrees of freedom, we determine the P-value.

DF = (r - 1) * (c - 1) = (4 - 1) * (5 - 1)
D.F = 12
E_r,c = (n_r * n_c) / n


Χ² = 7.5

where DF is the degrees of freedom.

The P-value is the probability that a chi-square statistic having 12 degrees of freedom is more extreme than 7.50.

We use the Chi-Square Distribution Calculator to find P(Χ² > 7.50) = 0.823

Interpret results. Since the P-value (0.823) is greater than the significance level (0.05), we have to accept the null hypothesis.

Thus, we conclude that there is no relationship between the region of the country and the categorical number of stores that have experienced at least a 20% rate of return of the item.