15. Fibonacci Meets Benford The Fibonacci sequence is a famous sequence of numbe

Question

15. Fibonacci Meets Benford The Fibonacci sequence is a famous sequence of number whose elements occur in nature quite often. You will probably recognize the sequence by looking at the first few terms:1, 1, 2, 3, 5, 8, 13, 21 Each term, starting with the third term, is simply the sum of the preceding two terms. The table below shows the observed counts of the left-hand digit for the first 125 terms of the Fibonacci sequence. Left-hand Observed Count 37 23 16 Digit 7 aw is P(occurrence of the left hand DI), run a Digit statistical Goodness of Fit Test" to see if the first 125 terms of the Fibonacci sequence follow Benford's Law. State your P-value from your analysis and what your final brief conclusion would be (using easy-to- understand language and your personally chosen level of significance ).

Explanation / Answer

H0: The observed counts follows Benford's Law or fibonacci squence

H1: The observed counts not follows Benford's Law or fibonacci squence

Let the los be alpha = 5%

Num Categories: 9
Degrees of freedom: 8

Test Statistic, X^2: 1.0157
Critical X^2: 15.5073
P-Value: 0.9981

Here P-value > alpha 0.05, so we accept H0

Thus we conclude that the observed counts follows Benford's Law or fibonacci squence

Left Hand Observed Expected Digit Count (Oi) Prob Count (Ei) (Oi-Ei)^2/Ei 1 37 0.30103 37.62874946 0.010505953 2 23 0.176091 22.01140738 0.044400403 3 16 0.124939 15.61734208 0.009375929 4 11 0.09691 12.11375163 0.102399547 5 11 0.079181 9.897655756 0.122772792 6 7 0.066947 8.368348704 0.223745238 7 7 0.057992 7.248993372 0.008552594 8 8 0.051153 6.394065306 0.403346872 9 5 0.045757 5.71968632 0.090555385 Total : 125 125 1.015654715

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