Former Democratic Presidential candidate Bernie Sanders is still pushing his vis

Question

Former Democratic Presidential candidate Bernie Sanders is still pushing his vision of a Scandinavian-like socialist utopia for America, despite dropping out of the race. Using the cornet.xlsx data file, I ran descriptive statistics on all three of the Scandinavian countries (finland, norway, and sweden) as well as usa. The resulting descriptive statistics were calculated: usa ~ N(0.0135, 0.0011) scandinavia ~ N(0.0131, 0.0034) R_usa, acandinavia = 0.4565 n = 107 Suppose someone makes the following claim: "The return of usa will exceed the return of scandinavia by approximately 10% this coming year." What is the probability that this statement is true, Pr(usa - scandinavia > 0.10)? Bernie claims that scandinavia > usa. Suppose we want to claim the opposite (that is, usa > scandinavia or usa - scandinavia > 0). Perform a hypothesis test to determine the validity of our claim.

Explanation / Answer

I will solve only Qn 14 as per Chegg Policy to make it a sufficient solution.

Now, X - Y follows Normal Distribution with:

mean mu = E(X) - E(Y) = 0.0135 - 0.0131 = 0.0004

and

Var(X-Y) = Var(X) + Var(Y) + 2 * Correlation * sqrt( Var(X) * Var(Y) )

= 0.0011^2 + 0.0034^2 - 2*0.0011*0.0034*0.4565

= 9.35538e-6

Hence, Std Dev(X-Y) = sqrt(Var(X-Y)) = sqrt(9.35538e-6) = 0.00305865657 = 0.0031 (almost)

Hence, answer is: P(X-Y > 0.10)

= 1 - P(X-Y<=0.10)

= 1- 1 = 0

Use normdist function of excel here.

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