Explanation Calculation: The given information is that, the sample size is 20 and parameter estimates are given below: b 0 = 1.05 , b 1 = 4.50 , s e = 0.54 , ∑ ( x − x ¯ ) 2 = 10.9 and x ¯ = 8.52 . Construction of confidence interval: y ^ ± t α 2 ⋅ s e 1 n + ( x ∗ − x ¯ ) 2 ∑ ( x − x ¯ ) 2 Where, A particular value of x ∗ is substituted to get the confidence interval. s e represents the residual standard deviation. x ¯ represents the mean of predictor variable. t α 2 represents the table value of t distribution for a given level of significance. From the given information the predicted value is calculated as follows: y ^ = b 0 + b 1 x * Substitute b 0 as 1.05, b 1 as 4.50 and x * as 10. y ^ = b 0 + b 1 x * = 1.05 + ( 4.50 ) ( 10 ) = 1.05 + 45 = 46.05 Thus, the predicted value y ^ is 46.05. Critical value: Software procedure: Step-by-step procedure to find the critical value using MINITAB is given below: Choose Graph > Probability Distribution Plot choose View Probability > OK. From Distribution , choose ‘ t ’ distribution. In Degrees of freedom , enter 18 . Click the Shaded Area tab. Choose Probability and Two tail for the region of the curve to shade. Enter the Probability value as 0.05 . Click OK . Output obtained from MINITAB is given below: Thus, the critical value t α 2 is 2

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Chapter 11.4, Problem 1CYU

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Construct the 95% confidence interval for the mean response when x=10.

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Chapter 11.3, Problem 31E

Chapter 11.4, Problem 2CYU

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Construct the 95% confidence interval for the mean response when x = 10 .

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Construct the 95% confidence interval for the mean response when x=10.

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