Question

You land a job at online marketing/consulting firm after attaining a business degree with an emphasis in statistics. You walk into your office on the first day and there is an assignment sitting upon your desk. The firm was recently hired by ImpulseBuyNow.com(a famous online clearing house for as-seen-on TV junk items). ImpulseBuyNow wanted to know if the amount of time spent browsing by a customer at their online site associates to how many items the customer purchased. Realizing that you listed a statistical emphasis in your business degree, you panic and pull out your old statistics notes as to find out this unit in the study guide. What luck! You must figure out what to tell ImpulseBuyNow about their question. here is the data.

Items Purchased

Browse Time (min) Zero One Two

0 to10 minutes. 1000 900 100

10 to 20 minutes

1500 2600 500

more than 20 minutes

500 2500 400

You paycheck depends upon whether or not you can figure if time spent browsing ImpulseBUyNow's website is associated with the numbers of items purchased by a customer. Figure this problem out, report your work, findings, and thoughts to the group. Below are a few hints so you can check your work. The first row of the expectation values should be: Expected Values Browse Time (min) Zero One Two

0 to 10 minutes

600 1200 200

And your final p-value is extremely small. Good luck and hopefully you will avoid a ramen noodle diet while looking for a new job.

Answer 1

We will perform a chi-square test to test the association between the two variables.

Null Hypothesis: There is no association between the browsing time & no. of items purchased

The data table is:

Browse Time	Zero	One	Two	Total
0-10	1000	900	100	2000
10-20	1500	2600	500	4600
More than 20	500	2500	400	3400
Total	3000	6000	1000	10000

We have the observed values of the above variables. We want to know the expected values so that we could have a statistical test whether the observed value deviates from the expected values. Then, we could make a claim whether there is an association between the browsing time and the number of items purchased. Hence, let's calculate the expected values & calculate the chi-square statistic given by the formula:

To calculate the expected values for a cell, we multiply the corresponding row and column total & then divide it by the overall total. For example, when Browsing time = 10-20 and Items bought = 2, Expected value = 1000*4600/10000 = 460. Hence, the expected values are:

Browse Time	Zero	One	Two	Total
0-10	600	1200	200	2000
10-20	1380	2760	460	4600
More than 20	1020	2040	340	3400
Total	3000	6000	1000	10000

Now, let's put the observed and expected values in a table and calculate the chi-square statistic:

Observed (O)	Expected E	O-E	(O-E)^2	(O-E)^2/E
1000	600	400	160000	266.6667
1500	1380	120	14400	10.43478
500	1020	-520	270400	265.098
900	1200	-300	90000	75
2600	2760	-160	25600	9.275362
2500	2040	460	211600	103.7255
100	200	-100	10000	50
500	460	40	1600	3.478261
400	340	60	3600	10.58824
			Total	794.2668

Chi-square statistic is 794.2668. The p-value corresponding to the chi-square statistic is extremely small (from the chi-square table at df = 2*2 = 4. Hence, we can reject the null hypothesis that there is no association between the variables. Therefore, we can conclude that there is an association between the browsing time and number of items purchased.