1. given the following dataset, from an experiment investigating the effect of keyboard type (variable X, four types) on student typing performance (Y is the number of errors made in typing up a document), each keyboard type was tested on 5 different students (between-subjects design).

	Yi1	Yi2	Yi3	Yi4	Yi5
X = 1	14	13	14	14	11
X = 2	13	12	10	14	12
X = 3	13	20	18	16	20
X = 4	17	19	18	16	18

1. In a standard ANOVA model 1 described as Y_ij = +_i +e_ij, compute the value of and_ifor i=1 and 3.

2. Provide the numerical values of MS_treatment and MSE.

3. Based on the analysis of the above data ( use JMP for this purpose), which keyboard would be recommended, and why? ( state the hypotheses, test statistics, decision rules, any posthoc tests that is constructed, and final conclusions. also list any assumptions that was made). show all the JMP outputs to justify the result.

4. Perform model diagnostics and report the findings, on whether the main assumptions for an ANOVA model were met.

use JMP to compute and show all the workings and JMP outputs.