Question

2) You have been asked to study whether there are any differences in the proportions of stores that have experienced a return rate of the shirt over the recent period of at least 20% based upon the region of the country where the stores are located. Random samples of stores in four regions of the country are selected. The sample data concerning whether the store has experienced a return rate of at least 20% for the item over the given time-period is shown in appendix two below. At each of the 5% and 2% levels of significance, are there any differences in the proportions of the stores in the various parts of the country concerning their having experienced at least a 20% return of the item over the period that is being studied? If at either significance level you find any differences in the proportions of the stores based upon location that have experienced at lease this return rate, perform the necessary work to ascertain where any possible differences lie. Appendix Two: Region ≥20% return One Two Three Four Yes 28 37 29 43 No 52 43 66 47

Answer 1

In the given question ,we are required to

1.Check if the proportions of two samples given are significantly different (4 regions)?

The level of significance being 5% and 2 % each .

This is a case of hypothesis testing of checking of difference between two sample proportions.

The sample proportions in two scenario (samples for the four regions 91,2,3,4) are :-

	Regions
	1	2	3	4
Yes	28	37	29	43
No	52	43	66	47

Now we shall perform hypothesis testing on each region.

Kindly note that we are given with percentage proportions in each case only . Hence we shall take into account that the sample size in each case is 100.