1.    The table below presents two sets of forecast errors determined based on the forecasts made using two different forecasting methods.

 Week

Forecast Errors

  Method 1

Method2

  1

5

8

  2

3

4

  3

-4

-1

  4

4

2

(a)  Determine the respective MADs for Method 1 and Method 2. For each MAD, please provide at least one step of calculation and the correct answer for full credit. (8 points)

MAD=(∑|Forecast Error| )/n

Method1  

=(5+3+-4+4)/4=2

Method 2

=(8+4+-1+2)/4= 3.25

(b) Determine the respective MSEs for Method 1 and Method 2.  For each MSE, please provide at least one step of calculation and the correct answer for full credit. (8 points)

MSE=(∑|Forecast Error| ) ^2 /n

Method 1: (25+9+16+26) = 66/4= 16.5

Method 2: (64+16+1+4) = 85/4=21.25

(c)  Which forecasting method is more accurate based on MAD? And which forecasting method is more accurate based on MSE? (4 Points)

1.    The results of an inspection of DNA samples taken over the past 10 days are given below. Sample size is 50.  

 Day

1

2

3

4

5

6

7

8

9

10

  # of defectives

2

1

3

2

0

4

3

5

0

2

(a) Determine the fraction defective of the p chart. Please give the formula and at least one step of calculation for full credit. (6 points)

Total # defective= 2+1+3+2+0+4+3+5+0+2= 22

Total # sampled= 50 x 10 = 500

= 22/500 = 0.044

(b) Determine the   of the p chart. Please give the formula and at least one step of calculation for full credit. (6 points)

n = sample size = 50  

σp = Öp (1 -   p)/n

= Ö0.44(1-0.44)/50

= 0.005

(c) Determine the 3-sigma upper control limit and the 3-sigma lower control limit of the p chart. For each control limit, provide at least one step of calculation and the correct answer for full credit. (8 points)

Z= 3

UCL=    +z  = 0.044 + (3)0.005 = 0.194

(a)  Is the DNA collection process under statistical control? Why and why not? (4 points)

Hello,  

I've send 2 questions that I have already answered them. only the once which are in red color I need help with them