[SOLUTION] Hypothesis Testing the Golden Ratio

The Golden Ratio, sometimes referred to as Phi (, is a ratio between two lengths A and B that yield the exact number  which is irrational and is approximately We will use 1.62 as our approximation for the purposes of this hypothesis test. Many claims have been made that the golden ratio exists in nature both in living and non-living things.For example, the length of a human arm from elbow to wrist compared to the length of the hand from wrist to tip of middle finger. In this example, the length from elbow to wrist would be length A and the length from wrist to middle finger would be length B.To test a claim such as this, suppose we collected a large data set and fond the mean average ratio for all the ratios collected to be 1.71. This is indeed close to 1.62, but do we then agree with the claim that human arms and hands grow in an approximate golden ratio? What if the original claim was that this human ratio was  which is approximately ?  Do our findings support this claim? This example shows why we never, ever support the null hypothesis with our findings. We may only reject it due to strong evidence to the contrary, or fail to reject it due to insufficient evidence to the contrary.

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