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Statistical Hypothesis Testing, Time Series Analysis, and Simple Linear Regression

## Statistical Hypothesis Testing for Marketing Research

Discussion In the research process for Frito-Lay Company, many different numerical questions were raised regarding Frito-Lay products, advertising techniques, and purchase patterns among Hispanics. In each of these areas, statistics—in particular, hypothesis testing—plays a central role. Using the case information and the concepts of statistical hypothesis testing, discuss the following:

1.1 Many proportions were generated in the focus groups and market research that were conducted for this project, including the proportion of the market that is Hispanic, the proportion of Hispanic grocery shoppers that are women, the proportion of chip purchasers that are teens, and so on. Use techniques you learned to analyze each of the following and discuss how the results might affect marketing decision makers regarding the Hispanic market.

a. The case information stated that 63% of all U.S. Hispanics are Mexican American. How might we test that figure? Suppose 850 U.S. Hispanics are randomly selected using U.S. Census Bureau information. Suppose 575 state that they are Mexican Americans. Test the 63% percentage using an alpha of .05.

b. Suppose that in the past, 94% of all Hispanic grocery shoppers were women. Perhaps due to changing cultural values, we believe that more Hispanic men are now grocery shopping. We randomly sample 689 Hispanic grocery shoppers from around the United States and 606 are women. Does this result provide enough evidence to conclude that a lower proportion of Hispanic grocery shoppers now are women?

c. What proportion of Hispanics listen primarily to advertisements in Spanish? Suppose one source says that in the past the proportion has been about .83. We want to test to determine whether this figure is true. A random sample of 438 Hispanics is selected, and the Minitab results of testing this hypothesis are shown here. Discuss and explain this output and the implications of this study using = .05.

1.2 The statistical mean can be used to measure various aspects of the Hispanic culture and the Hispanic market, including size of purchase, frequency of purchase, age of consumer, size of store, and so on. Use techniques you learned to analyze each of the following and discuss how the results might affect marketing decisions.

a. What is the average age of a purchaser of Doritos Salsa Verde? Suppose initial tests indicate that the mean age is 31. Is this figure really correct? To test whether it is, a researcher randomly contacts 24 purchasers of Doritos Salsa Verde with results shown in the following Excel output. Discuss the output in terms of a hypothesis test to determine whether the mean age is actually 31. Let be .01. Assume that ages of pur-chasers are normally distributed in the population.

## Proportion Testing

b. What is the average expenditure of a Hispanic customer on chips per year? Suppose it is hypothesized that the figure is \$45 per year. A researcher who knows the Hispanic market believes that this figure is too high and wants to prove her case. She randomly selects 18 Hispanics, has them keep a log of grocery purchases for one year, and obtains the following figures. Analyze the data using techniques from this chapter and an alpha of .05. Assume that expenditures per customer are normally distributed in the population

Section Two

Time Series

For this activity, select a recurring quantity from your own life for which you have monthly records at least 2 years. This might be the cost of a utility bill, the number of cell phone minutes used, or even your income. If you do not have access to such records, use the internet to find similar data, such as average monthly housing prices, rent prices in your area for at least 2 years. Data can also be monthly sales of some particular commodity.

2.1 Which methods in our Chapter TIME SERIES might apply to your data? Does there appear to be a seasonal component affecting the data? If so, can you explain the seasonal effect in simple terms?

2.2 Use methods you learned to predict the value of your quantity for the next year. Be prepared to defend your choice if methods.

Section Three

Applying Simple Linear Regression to Your favorite Data

Many dependent variables in business serve as the subjects of regression modeling efforts. We list such variables here:

Rate of return of a stock

Annual unemployment rate

Grade point average of an accounting student

Gross domestic product of a country

Salary cap space available for your favorite NFL team

Choose one of these dependent variables, or choose some other dependent variable, for which you want to construct a prediction model. There may be a large number of independent variables that should be included in a prediction equation for the dependent variable you choose. List three potentially important variables, 1, 2, and 3, that you think might be (individually) strongly related to your dependent variable. Next, obtain 25 data values, each of which consist of a measure of your dependent variable and the corresponding values of 1, 2, and  3.

3.1 Use the least squares formulas given in our chapter to fit three straight-line models-one for each independent variable- for predicting .

3.2 Interpret the sign of the estimated slope coefficient 1 in each case, and test the utility of each model by testing 0: 1 = 0 against : 1 ≠ 0. What assumptions must be satisfied to ensure the validity of these tests?

3.3 Calculate the coefficient of determination, 2, for each model. Which of the independent variables predicts best for the 25 sampled sets of data? Is this variable necessarily best in general (i.e., for the entire population)? Explain.