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# Coffee Time Case Study: Type I and Type II Errors

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CoffeeTime has made great strides in gaining market share in Mumbai. In order to maximize our profit potential in this challenging market, it will be necessary to carefully analyze predictors of increased revenue so that we do not spend on unnecessary advertising or raise prices out of proportion to the market. Therefore, we have used historical data to build what is called a multiple regression model to help us predict how revenues will be impacted by other independent variables.
With this model, we can analyze the affect on revenue of changing one or more of our variables while keeping other variables constant. After running several scenarios, we have concluded there are five significant independent variables that affect our dependent variable which is revenue. These include:
Coffee Times weekly advertising expenditure, Coffee Times weekly advertising expenditure (lagged), Coffee Times price index, Coffee Times price index (Lagged), and Estimate on Quick brews weekly advertising expenditure (lagged).
The equation we have developed to predict effects on revenue when one or more of the independent variables is increased or decreased is:
Y = 246,491.990 + 4.556X1 - 699.171X2 + 5.719X4 - 624.925X5 - 1.729X6
Y = Predicted weekly revenue
X1 = Coffee Times weekly advertising expenditure
X2 = Coffee Times price index
X4 = Coffee Times weekly advertising expenditure (lagged)
X5 = Coffee Times price index (Lagged)
X6 = Estimate on Quick brews weekly advertising expenditure (lagged)
The local management can now use this model to make decisions regarding advertising and pricing while better understanding how Quick Brew's advertising expenditures will impact CoffeeTime revenues.
During the research, a test was performed on the independent variables to assess whether a condition called multicollinearity exists between two or more of the variables. This is a "situation where two or more of the independent variables are highly correlated (and) can have damaging effects on multiple regression" (Cooper and Schindler, 2003, p. 617).
The analysis showed that the correlation between Coffee Times weekly advertising expenditure (lagged) and the Estimate on Quick brews weekly advertising expenditure (lagged) was fairly high at 0.65. However, since we determined to base our decision to remove any independent variables with correlations higher than 0.70, we will not remove any of them.
Before launching any type of product, it is extremely beneficial for businesses to find out if there is a need or a want for the product. Since Coffee Time's successful launch of their Coffee shop in India, they have decided to introduce a new product to increase sales and profits and would like to establish a want of 30% or more for the product to make it cost effective to launch.
In order to determine if 30% of India's population proportion would like the new sandwich, CoffeeTime has used a hypothesis and a Z-test to resolve this argument. Below you will find the hypothesis used, and other variables,
Ho: P&#8804;0.30 Level of significance: 20% or 0.20
H1: P>0.30 Type of test: Z-test / one tailed test
Sample size: 160 Z= -1.656
Critical Value Z= .84 Accept the null hypothesis
With the analysis done it is seen that CoffeeTime can accept the null hypothesis of p&#8804;0.30, which means that the population proportion is either less than or equal to 30% that likes the new sandwiches, since the z-score created is less than the critical value (Z) and does not fall within the rejection zone. This information is critical for the managers of CoffeeTime to make their decisions on whether to launch or not to launch the new product for the following reason.
During the testing, the company was concerned about the type of error that could occur, type 1 error, "rejecting the null hypothesis, H0, when it is true" or a type II error, "accepting the null hypothesis when it was false" (Lind, 2004, p320).

Within the two types of error, it would be more costly for CoffeeTime to have a type II error and launch the new product when there is no demand for it. What is your insight on this outcome. Can you sum it up for me. Thanks