Question

One of the items that businesses would like to be able to test is whether or not a change they make to their procedures is effective. Remember that when you create a hypothesis and then test it, you have to take into consideration that some variance between what you expect and what you collect as actual data is because of random chance. However, if the difference between what you expect and what you collect is large enough, you can more readily say that the variance is at least in part because of some other thing that you have done, such as a change in procedure.

For this submission, you will watch a video about the Chi-square test. This test looks for variations between expected and actual data and applies a relatively simple mathematical calculation to determine whether you are looking at random chance or if the variance can be attributed to a variable that you are testing for.

Imagine that a company wants to test whether it is a better idea to assign each sales representative to a defined territory or allow him or her to work without a defined territory. The company expects their sales reps to sell the same number of widgets each month, no matter where they work. The company creates a null and alternate hypothesis to test sales from defined territory sales versus open sales.

One of the best ways to test a hypothesis is through a Chi-square test of a null hypothesis. A null hypothesis looks for there to be no relationship between two items. Therefore, the company creates the following null hypothesis to test: There is no relationship between the amount of sales that a representative makes and the type of territory (defined or open) that a representative works in. The alternate hypothesis would be the following: There is a relationship between the kind of sales territory a sale representative has (defined or open) and the amount of sales he or she makes during a month.

Step 1:

Watch this video.

Step 2:

Use the following data to conduct a Chi-square test for each region of the company in the same manner you viewed in the video:

Region	Expected	Actual
Southeast
Defined	100	98
Open	100	104
Northeast
Defined	150	188
Open	150	214
Midwest
Defined	125	120
Open	125	108
Pacific
Defined	200	205
Open	200	278

Step 3:

Write an 800–1,000-word essay, utilizing APA formatting, to discuss the following:

• Describe why hypothesis testing is important to businesses.
• Report your findings from each Chi-square test that you conducted.

Answer 1

Step 2:

The Chi-square test of independence is performed to test whether the amount of sales that a representative makes is associated with the type of territory (defined or open).

For Southeast

The Chi-Square value is obtained using the formula

Observed	Expected
98	100	-2	4	0.04
104	100	4	16	0.16
				0.2

The critical value for the chi-square statistic is obtained from the chi-square distribution table for,

Where r is the number of rows and c is the number of column in the table.

For significance level = 0.05 and degree of freedom = 12, the critical value is,

Conclusion:

Since the chi-square value is less than the critical value, It can be concluded that the null hypothesis is not rejected at a 5% significance level.

Hence both the variables are independent for the southeast region.

For Northeast

The Chi-Square value is obtained using the formula

Observed	Expected
188	150	38	1444	9.63
215	150	65	4225	28.17
				37.79

Conclusion:

Since the chi-square value is greater than the critical value, It can be concluded that the null hypothesis is rejected at a 5% significance level.

Hence both the variables are dependent for the northeast region.

For Midwest

The Chi-Square value is obtained using the formula

Observed	Expected
120	125	-5	25	0.2
108	125	-17	289	2.312
				2.512

Conclusion:

Since the chi-square value is less than the critical value, It can be concluded that the null hypothesis is not rejected at a 5% significance level.

Hence both the variables are independent for the midwest region.

For Pacific

The Chi-Square value is obtained using the formula

Observed	Expected
205	200	5	25	0.125
278	200	78	6084	30.42
				30.545

Conclusion:

Since the chi-square value is greater than the critical value, It can be concluded that the null hypothesis is rejected at a 5% significance level.

Hence both the variables are dependent for the pacific region.