A random sample of 309 lunch customers is taken, resulting in the following results. Determine whether the two variables are independent at 95% level of significance. (4 points)

The p value is .000, which is lower than 0.05 suggests a relationship between age and type of beverage. The null hypothesis is thus rejected and the conclusion is that type beverage and age are related.

3. In one survey, successful women meeting managers were asked to state their personal definition of success in terms of several categories from which they could select. Thirty-nine percent responded that happiness was their definition, 12% said that sales/profit was their definition, 18% responded that helping others was their definition, and 31% responded that achievement/challenge was their definition of success. Suppose that you want to determine whether men meeting managers felt the same way and took a random sample of men meeting managers, resulting in the data shown. Use the Chi-square test to determine whether the observed frequency distribution of data for men meeting managers is the same as the distribution for women meeting managers. Let α = .05. (4 points)

The test statistics table shows a very small computed Chi-square value 201.56 and a very small p-value 0.00, which is smaller than 0.05. Therefore, H0 is rejected, and hence there is a difference between the successful women and those who were randomly sampled.

4. Is there a relationship between having a lap-top computer and a person’s profession? A survey of 187 managers of three professions: travel manager, lawyers and accountants, was conducted to investigate this question. Results are presented in the following table. Test whether having a lap-top computer is independent of profession at 95% level of significance.