Given Information:
Mean = 1500
Standard Deviation = 400

Increment in the first year = 100

Hike in each observation by 20% in the second year

To find:
New Mean and New Standard Deviation

Solution:
1. Increment in the First Year:
Since the increment is the same for all the observations, the new mean will be the sum of the old mean and the increment.

New Mean = Old Mean + Increment
New Mean = 1500 + 100
New Mean = 1600

2. Hike in each observation by 20% in the Second Year:
To find the new standard deviation, we need to find the new values of each observation after the hike of 20%.

Let's assume the old observations as x1, x2, x3, ..., xn

The new observations will be x1*(1+20%), x2*(1+20%), x3*(1+20%), ..., xn*(1+20%)

Simplifying the above expression, we get:

New Value of observation = Old Value of observation * 1.2

Now, we can find the new mean and new standard deviation using the new values of observations.

3. New Mean:
New Mean = Sum of New Values of Observations / Total Number of Observations

We know that the total number of observations is the same as before. So, we just need to find the sum of new values of observations.

Sum of New Values of Observations = x1*1.2 + x2*1.2 + x3*1.2 + ... + xn*1.2
Sum of New Values of Observations = 1.2(x1 + x2 + x3 + ... + xn)
Sum of New Values of Observations = 1.2 * Sum of Old Values of Observations

Therefore, New Mean = 1.2 * Old Mean
New Mean = 1.2 * 1600
New Mean = 1920

4. New Standard Deviation:
To find the new standard deviation, we need to find the sum of squares of the deviations of each new value from the new mean.

Sum of Squares of Deviations from New Mean = (x1*1.2 - 1920)^2 + (x2*1.2 - 1920)^2 + ... + (xn*1.2 - 1920)^2

We can simplify the above expression as follows:

Sum of Squares of Deviations from New Mean = 1.44[(x1 - 1600)^2 + (x2 - 1600)^2 + ... + (xn - 1600)^2]

We know that the last term in the above expression is the same as the old standard deviation squared.

Therefore, Sum of Squares of Deviations from New Mean = 1.44 * (Sum of Squares of Deviations from Old Mean) + (Old Standard Deviation)^2

Now, we can find the new standard deviation using the following formula:

New Standard Deviation = Square Root of [Sum of Squares of Deviations from New Mean / Total Number of Observations]

New Standard Deviation = Square Root of [1.44 * (Sum of Squares of Deviations from Old Mean) + (Old Standard Deviation)^2 / Total Number of Observations]

New Standard Deviation =