In the regression equation, ŷ = 2.164 + 1.3657x, and n = 6, the mean of x is 8.667, SS_xx= 89.333 and S_e= 3.44.A 95% confidence interval for the average of y when x=8 is _________ A)(9.13, 17.05) B)(2.75, 23.43) C)(10.31, 15.86) D)(3.56, 22.62) E)(12.09, 14.09)

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The correct answer is A because the confidence interval is (9.13, 17.05). The confidence interval is calculated using the formula:ŷ ± t_{(n-2, α/2)} * S_e * √(1/n + (x - x̄)²/SS_xx)where:ŷ is the predicted value of yt_{(n-2, α/2)} is the t-value for the desired confidence level and degrees of freedomS_e is the standard error of the estimaten is the sample sizex is the value of x for which we are predicting yx̄ is the mean of xSS_xx is the sum of squares for xPlugging in the given values, we get:ŷ ± t_{(4, 0.025)} * 3.44 * √(1/6 + (8 - 8.667)²/89.333)= 12.59 ± 3.96 * 0.98= (9.13, 17.05)

In the Regression Equation, ŷ = 2