5.5 Table 5.15 shows a regression output obtained from fitting the model Y = Bo +...

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5.5 Table 5.15 shows a regression output obtained from fitting the model Y = Bo + B₁X + ε to a set of data consisting of n workers in a given company, where Y is the weekly wages in $100 and X is the gender. The Gender variable is coded as 1 for Males and 0 for Females. Table 5.15 Regression Output from the Regression of the Weekly Wages, Y, on X (Gender: 1 = Male, 0 = Female) Source Regression Residual Variable Constant X Sum of Squares 98.8313. 338.449 Coefficient 15.58 -2.81 ANOVA Table df 1 48 Coefficients Table s.e. 0.54 0.75 Mean Square 98.8313 7.05101 t-Test 28.8 -3.74 F-Test 14 p-value <0.0001 0.0005 (a) How many workers are there in this data set? (b) Compute the variance of Y? (c) Given that x = 0.52, what is y? (d) Given that x = 0.52, how many women are there in this data set? (e) What percentage of the variability in Y can be accounted for by X? (f) Compute the correlation coefficient between Y and X? (g) What is your interpretation of the estimated coefficient 31? (h) What is the estimated weekly wages of a man chosen at random from the workers in the company? (i) What is the estimated weekly wages of a woman chosen at random from the workers in the company? (i) Construct a 95% confidence interval for B1. (k) Test the hypothesis that the average weekly wages of men is equal to that of women. [Specify (a) the null and alternative hypotheses, (b) the test statistics, (c) the critical value, and (d) your conclusion.] 5.5 Table 5.15 shows a regression output obtained from fitting the model Y = Bo + B₁X + ε to a set of data consisting of n workers in a given company, where Y is the weekly wages in $100 and X is the gender. The Gender variable is coded as 1 for Males and 0 for Females. Table 5.15 Regression Output from the Regression of the Weekly Wages, Y, on X (Gender: 1 = Male, 0 = Female) Source Regression Residual Variable Constant X Sum of Squares 98.8313. 338.449 Coefficient 15.58 -2.81 ANOVA Table df 1 48 Coefficients Table s.e. 0.54 0.75 Mean Square 98.8313 7.05101 t-Test 28.8 -3.74 F-Test 14 p-value <0.0001 0.0005 (a) How many workers are there in this data set? (b) Compute the variance of Y? (c) Given that x = 0.52, what is y? (d) Given that x = 0.52, how many women are there in this data set? (e) What percentage of the variability in Y can be accounted for by X? (f) Compute the correlation coefficient between Y and X? (g) What is your interpretation of the estimated coefficient 31? (h) What is the estimated weekly wages of a man chosen at random from the workers in the company? (i) What is the estimated weekly wages of a woman chosen at random from the workers in the company? (i) Construct a 95% confidence interval for B1. (k) Test the hypothesis that the average weekly wages of men is equal to that of women. [Specify (a) the null and alternative hypotheses, (b) the test statistics, (c) the critical value, and (d) your conclusion.]