Introduction
Statistical hypothesis tests involve using of a sample statistic from a sample of the total population to estimate the eventual probability that a tested population parameter is equal to a particular value, often zero. In hypothesis testing, there would be a prediction derived from a model or theory that is the null hypothesis and an alternate hypothesis which is an exact opposite of the null hypothesis.
Question one
For businesses to stay afloat and keep up with competition, they need to constantly improve their services, goods and as well as marketing strategy based on the needs of the various stakeholders involved. Therefore, in order for the business to make the best decisions that will improve their revenues, they need to not only collect data from various regions or sectors served by the business but also do analysis on the data and interpret accordingly to plan their activities better. An important way of analyzing a set of data is through hypothesis testing. Hypothesis testing uses sample statistics to test a claim about a parameter.
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For example, let’s say a company wants to increase sales by funding a new marketing campaign. It therefore decides to use this campaign in a specific region and collects data from that region to see whether the campaign has the desired effect. The effect in this case, and in order for it to continue the new marketing campaign nationally, the sales need to raise by more than 25%. To test this, the company can perform hypothesis testing on the sample data collected from the test region. The company can therefore carefully examine the results and make optimal business decisions that will have a profound impact on its future operations.
Question two and three
There can only be possible outcomes in this case, defined or open territory in each region therefore the degrees of freedom becomes:
With the probability of exceeding the critical value set at 0.05, the critical value becomes 
In the South East region,
Using the chi-squared test formula:
Since 0.2 is smaller than the critical value of 3.841, we accept the null hypothesis.
In the North East region,
Using the same chi-squared test formula we can get the critical value from the following:
From the above calculations, the chi-squared value 36.933 is much higher than the critical value of 3.841. So, in this case, we accept the alternate hypothesis for the North East region and reject the null hypothesis.
In the Midwest region,
To get the critical value,
From the above calculations, the chi-squared value 2.512 is smaller than the critical value of 3.841. Therefore, in the Midwest region, we accept the null hypothesis.
In the Pacific region,
The chi-squared value obtained in this case is 30.545, it is significantly higher than the critical value of 3.841. Therefore, we accept the alternate hypothesis and reject the null hypothesis.
Question four
The company should also consider doing the student’s t-test. The t-test can be used to determine between the difference between sales in different regions. The t value is a ratio of the difference between means of different data sets to the Square-root of the sum of the variance over the sample tally. The t-value is then compared to the value the critical value in the t-table and from this table, we can determine whether to accept the null hypothesis or reject the null hypothesis. If the t-value is less than the critical value then we accept the null hypothesis. However, if the t-value greater than the critical value then reject the null hypothesis. Therefore, here the company will be able to set hypothesis that analyzes different factors that affect different regions and make a conclusion that would be useful in deciding whether to go with the defined or open sales strategy.
The Analysis of Variance (ANOVA) test should also be considered before reaching a conclusion. ANOVA tests the difference between group means after any other variance in the outcome variable is accounted for.
Question five
Chi square test would be useful to a company that wants to determine what products sell better in certain geographical locations than others. In this case different types of products are examined and are analyzed to come up with an appropriate business decision. A good example would be: the type of shoes that sold during winter would be dependent on whether a retail outlet is located in the upper mid-west versus in the south of America.
Conclusion
Chi square test analysis was used to determine whether the company should have defined territories for various employees or have an open territory for all. The null hypothesis was that there is no relationship between amount of sales that a representative makes and the type of territory that a representative works in. The alternate hypothesis therefore was there is a relationship between the kind of sales territory a sale representative has and the amount of sales he or she makes during a month. From the calculations, it was found that in some regions that is the mid-west and south-east regions, the null hypothesis was accepted. In the rest of the regions; North East and Pacific regions the null hypothesis was rejected and the alternate hypothesis was accepted.
REFERENCE
Quinn, G., & Keough, M. (2002). Statistical hypothesis testing. Experimental design and data analysis for biologists , 2002 , 32-39.
Bozeman Science. (2011, November 13). Chi-squared test [Video file]. Retrieved from https://www.youtube.com/watch?v=WXPBoFDqNVk
