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sample Size determination
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## Explanation on how the sample sie was determined
Sample Size formula from cuemath.com https://www.cuemath.com/sample-size-formula/
##Section referenced
Using the Standard Formula
Lets' look at the below-given equation. If the size of the population is small to moderate, then it is easier to know all the key values and thus the standard formula can be used. The standard formula for calculating the sample size is:
Sample Size Formula = [z2 * p(1-p)] / e2 / 1 + [z2 * p(1-p)] / e2 * N]
Where:
z is the critical value of the normal distribution at the desired confidence level
p is the estimated proportion of the attribute in the population
e is the margin of error
N is the population size
For our analysis I used the following
Desired Confidence Level : 99.99%
Margin of Error : 0.2%
Population Size:5,860,776 (this is the Total number of observations in the combined dataset that contains 12 months of cyclistyic data that is being used)
p:50%
Therefore
z=3.89
p=0.5
e=0.002
N= 5,860,776
#Sample size calculation
Sample Size = [3.89 2 * 0.5 (1-0.5)] / 0.002 2 / 1 + [3.89 2 * 0.5 (1-0.5)] / 0.002 2 * 5860776]
Sample Size = [7.5721 * 0.25] / 0.000004 / [1 + (7.5721 * 0.25) / (0.000004 * 5860776)]
Sample Size = [1.893025] / [1 + (4.68275) / (23)] Sample Size = [1.893025] / [1 + (0.203599)]
Sample Size = [1.893025] / [1 + (203599)]
Sample Size = [1 + (203599)]/[(203599)]
Sample Size = [(203600)]/[(203599)]
Sample Size ≈ 1104058