A survey of 55 Duke University students asked about their GPA, number of hours they study at night, number of nights they go out, and their gender. Summary output of the regression model is shown below. Note that male is coded as 1.

(a) Calculate a 95% confidence interval for the coefficient of gender in the model, and interpret it in the context of the data.

(b) Would you expect a 95% confidence interval for the slope of the remaining variables to include 0? Explain

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(Intercept) studyweek sleepnight outnight gender Estimate Std. Error 0.35 0.00 0.05 3.45 0.00 0.01 0.05 -0.08 0.05 0.12 t value 9.85 0.27 0.11 1.01 -0.68 Pr(>|t|) 0.00 0.79 0.91 0.32 0.50