Gasoline Demand Case Assignment

Quant Business Analysis

Excel Calculations:

Excel Sheet

Calculation of Average Consumption:

Sample Mean (x̄) = ( Σ xi ) / n

(x̄)= 291.8976

This is the average gas consumption calculated by adding up all the individual consumption values (Σ xi) and dividing by the total number of observations (n).

Standard Deviation (σ) = √(∑(x−x̄) ( x − x̄ ) ² /n)

(σ) = 273.3269

This measures how much the individual gas consumption values vary or spread out from the average (mean). A higher standard deviation means more variability. In this case, the standard deviation is 273.3 units, indicating quite a wide spread in household gas consumption.

Standard Error (SE) = S / √n

(SE) = 3.86504

This quantifies how precisely the sample mean estimates the true population mean. It’s calculated by dividing the standard deviation by the square root of the sample size (number of households). Here, the standard error is about 3.87 units, showing that the average consumption estimate is fairly precise because of the large sample size.

Confidence Interval (CI) = (x̄) ± (Z-score * (σ / √n))

This gives a range around the sample mean where we can be confident the true average gas consumption for the whole population lies.

* Z score is 1.96 for 95% confidence

Lower Bound = (x̄) - (Z-score * (σ / √n))

Upper Bound = (x̄) + (Z-score * (σ / √n))

(CI) = [ 291.8976 + (1.96 * (273.3269/√5002)), 291.8976 - (1.96 * 273.3269/√5002) ]

(CI) = [ 284.3221 , 299.4730 ]

OR

Confidence Interval (CI) = Point Estimate (x̄) ± Margin of Error (ME)

ME = (Z score * (S/√n))

This is the amount added and subtracted from the sample mean to create the confidence interval.

S = Sample Standard Deviation

n = Sample Size

* CV is 2 for 95% confidence

Lower Bound = PE (same as x̄) - (CV*SE)/ME

Upper Bound = PE + (CV*SE)/ME

(CI) = [ 291.8975−7.575, 291.8975+7.575 ]

(CI) = [ 284.3221 , 299.4730 ]

The interval calculated is approximately [284.3, 299.5] units. This means we are 95% confident that the true average household gas consumption lies between about 284.3 and 299.5 units

1) What this looks like in a Normal Distribution:

Based on the sample data, the average household gas consumption is about 291.9 units, but because of natural variability and sampling, the true average is likely between 284.3 and 299.5 units with 95% confidence.

2) A closer look:

Calculation of Urban Area Consumption:

Sample Mean: 269.689

Standard Deviation: 247.0472

Standard Error: 4.2455

95% Confidence Intervals: [261.3678, 278.0102]

1)

For urban households, we estimate the average gasoline consumption to be about 269.7 units, and we are 95% confident that the true average consumption lies somewhere between 261.4 and 278.0 units.

2)

Calculation of Single/ Young Consumption:

Sample Mean: 198.6967

Standard Deviation: 189.4223

Standard Error: 15.4662

Confidence Intervals: [168.3833, 229.0099]

1)

For households made up of young, single individuals, the estimated average gasoline consumption is around 198.7 units. We can be 95% confident that the true average consumption of this group falls between 168.4 and 229.0 units.

2)