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4. In an experiment to study the effect of the amount of baking powder in a biscuit dough upon the rise heights of the biscuits, four levels of baking powder were tested and four replicate biscuits were made with each level in a random order. The results are shown in the table below 25 tsp .5 tsp .75 tsp 1 tsp 11.4 27.847.661.6 11.0 29.247.0 62.4 11.3 26.8 47.3 63.0 9.5 26.045.563.9 (a) What is the experimental unit? (b) Perform the Analysis of Variance to test the hypothesis of no treatment effect (c) Formulate a contrast to test the hypothesis that increase in rise height is proportional to the increase in baking powder in the dough and test this hypothesis (d) Estimate the variance of the experimental error σ2 (e) Make a plot of residuals versus predicted values and normal plot of residuals and comment on whether the assumptions of the inear model are justified (f) If the dough were made in batches and the four replicate biscuit rise heights in each column (shown in the table above) were all from the same batch, would your answer to (a) be different? How could the data be analyzed if this were the case?I need an all of the answer for this question.

math   Statistics-And-Probability   
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Number of 16 experimental units: nrt- >n 16Data Matrix: X. -Data Total variation in one-way ANOVA c-1j C-1 ㄨㄧ˙- in-一 Σ Σ(Xi-X--=6159.219 36.956 SST:- Among group variation in one-way ANOVA S :Data 10.8 S_- sample mean of group j mean (Data-1 27.45 s_t 46.85 I 62.725 x -6145.7319 Within-group variation in one-way ANOVA n-1 Degrees of Freedom:Mean squares in one-way ANOVA SSA SSW SST MSA:- MSW:- MST: One-way ANOVA Fstat test statistic MSA stat MSW Analysis of Variance summary table: Source Degrees of freedonm Sum of squaresS Mean Squares (Variance) Regression dfA-3 Error Total SSA-6145.732 MSA 2048.577 Fstat 1822.6452 dfw- 12 SSW-13.488 MSW- 1.124 dfr-15 SST 6159.219Critical value of F distribution: 0.05 F-qF (-a),dfa,dfw)-3.4903 FstaưP, and p value < 0.05, so You reject null hypothesis. We conclude that there is a significant difference in the mean effects among the four different amounts of the baking powder in the biscuits. The p-value of 0.00 indicates that there is no chance of observing differences this larger or larger if the population means for the four different quantities of the baking powder are equal. It means that at least one of the quantities mean effect is different than the others. There is a zero chance of claiming that the groups mean effects are same.

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