Economics Problems With Solution 2022

Q1:
Detecting and removing errors from the data given
0 1 2 3 4 5 6 7 8 9 10
0
50
100
150
200
250
f(x) = 1.19 x³ − 11.09 x² + 27.8 x
R² = 0.99
Plot with error
My Data Curve
Error = (1-0.9895) x 100% = 1.05%

0 1 2 3 4 5 6 7 8 9 10
0
50
100
150
200
250
f(x) = x³ − 8.05 x² + 13.24 x + 18.89
R² = 1
Plot with error removed
My Data Curve
Error = (1-1) x 100% = 0%

Q2:
Plot for i=32+50 sin(314.2 t)+20 sin(628.4 t − π
2 )
The expected response was a sinusoidal wave centered at 32. However, due two two
different frequency components with different magnitudes, the current results in the
above waveform. The double frequency component lags by 180o which is the reason
why the frequency components do not superimpose each other in every half a cycle.
Q3:
High-Pass filter magnitude and phase response
The transfer function of an analog high-pass filter is:
sRC
1+ sRC = s
s+ 1
RC

Q4:
The z-score is defined as: z= x − ~x
σ
In this case, σ =0.9, x=13.5
(a) ~x < 12.0A, z= 13.5− 12
0.9 =1.67
The p-value for z < 1.67 is: 0.4525
(b) ~x between 12.5A and 13.0A
z 1=13.5 −12.5
0.9 =1.11
z 2=13.5 −13
0.9 =0.56
P = 0.3643 - 0.2123 = 0.1520
(c) ~x > 14
z= 13.5− 14
0.9 =− 0.56