(c) \((2\%)\) Use 0.05 as significance level and draw a conclusion.

2.2 (10%) Among 100 managers with degrees in business administration, the following data have been accumulated as to their fields of concentration. | Major | Position | | TOTAL | | --- | --- | --- | --- | | | Top Management | Middle Management | | | Management | 28 | 22 | 50 | | Marketing | 12 | 8 | 20 | | Accounting | 10 | 20 | 30 | | TOTAL | 50 | 50 | 100 | To test if the position in management is independent of field (major) of concentration, (a) (5%) State the null and alternative hypotheses.

(b) (5%) At 95% confidence using the p-value approach, test the hypotheses. What is your conclusion? (For the test, give the null and alternative hypotheses, test statistic, and conclusion.)

2.3 (10%)Employees of AAA Corporation are about to undergo a retraining program. Management is trying to determine which of three programs is the best. They believe that the effectiveness of the programs may be influenced by sex. A factorial experiment was designed. You are given the following information of score. Factor B (Sex) | Factor A (Program) | 1 | 2 | | --- | --- | --- | | A | 26 19 20 21 | 24 21 20 23 | | B | 30 24 25 29 | 33 27 31 29 | | C | 26 22 27 17 | 31 23 24 26 | Given SSA=184.33, SSB=28.17, SSAB=8.33, SST=405.83 (a) (5%) Set up the ANOVA table.

(b) (5%) What advice would you give AAA Corporation? Use

a .05 level of significance. (Hint: Test for any significant differences due to programs, sex, and interaction. For each test, give the null and alternative hypotheses, test statistics, and conclusion.) 2.4 (10%) Multiple regression analysis was used to study how an individual's income (Y in thousands of dollars) is influenced by age (X₁ in years), level of education (X₂ ranging from 1 to 5), and the person's gender (X₃ where 0=female and 1=male). The following is a partial result of computer output that was used on a sample of 20 individuals. | ANOVA | | | | | | --- | --- | --- | --- | --- | | | df | SS | MS | F | | Regression | | 84 | | | | Residual | | 112 | | | | Predictor | Coefficients | Standard Error of Coefficient | | | | Constant | 21.00 | 0.70 | | | | X₁ | 0.62 | 0.10 | | | | X₂ | 0.92 | 0.19 | | | | X₃ | -0.51 | 0.92 | | | (a) \((2\%)\) Present the estimated regression equation and compute the coefficient of determination. Explain it.

(b) (2%) Use the \(t\) test to determine the significance of each independent variable. Let \(\alpha = 0.05\). (For each test, give the null and alternative hypotheses, test statistic, and conclusion.)

(c) \((2\%)\) Use the \(F\) test to determine the whether or not the regression model is significant. Let \(\alpha = 0.05\). (For the test, give the null and alternative hypotheses, test statistic, and conclusion.)

(d) (2%) Does the estimated regression equation provide a good fit for the observed data? Explain it based upon the results from part (a), (b), and (c).

(e) (2%) Suppose a new person with \( X_{1} = 40 \), \( X_{2} = 4 \), \( X_{3} = 1 \). Use the estimated regression equation from part (a) to estimate the new person's income.

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