6 marks b propose a better design for this experiment

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Stating assumptions, test the null hypothesis that the mean taste scores for A and B are equal. [6 marks] b) Propose a better design for this experiment. Write precise instructions for the conduct of your preferred experiment. [4 marks] 3. Supose we fit a simple linear regression model of the form: i Y = ( ) 0 1 i i x x R β β + + , where ( ) ~ , i R G o σ , 1,2, , i n = independent and x is the average i i x n . a) Show that 1 ˆ 0 n i i r = = where ˆ i r is the estimated residual that results from the fit of a simple linear regression model using the “least squares” solution. [4 marks] b) Also show that 1 ˆ 0 n i i i x r = = . [4 marks] c) Distinguish and explain the difference between i) residual and standardized residual [2 marks] ii) ( ) 0 i E R = and 1 ˆ n i i r n = = 0 [2 marks]
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