Please solve either by hand or by using R programming.

3. Consider the hardness testing experiment. The machine operates by pressing the tip into a metal test coupon, and from the depth of the resulting depression, the hardness of the coupon can be determined. The experimenter has decided to obtain 4 observations on Rockwell C-scale hardness for each tip. There is only one factor (tip type) and a completely randomized blocking design (RCBD) with blocking factor (coupon). Coupon Tip 1 2 3 4 1 9.39.49.610 9.49.39.89.9 3 9.29.49.59.7 9.79.6 10 10.2 i. Suppose that the observation for Coupon 2 and Tip 3 is missing, please estimate the value of this missing observation. Find 95% confidence interval for Tip mean difference ii. Please use four Latin letter A, B, C, D to define the standard Latin square design (Please assign each letter to every observation) Coupon Tip 1 (letter) 2 3 1 93( )94( )9.6( )10 2 94( )93 ( )9.8( )9.9 3 9.2( )94( )95( )97 ( ) 4 97( )96( )10 ( ) 10.2 ( ) iii. If there is one missing value of the above tables, please estimated this missing value based on Latin Square Design. Latin Square (the missing value is denoted by "-"): Coupon Tip I (letter) 2 3 4 1 93( )9.4( )9.6( )10 ( ) 2 9.4 ( ) 93 ( )9.8 ( )- ( ) 9.2( )94( )95 ( )97 ( ) 4 97( ) 9.6( )10 ( )10.2( )