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An economist wishes to determine if a linear relationship exists between the returns of the S&P 500 and the Dow Jones Industrial Average.

Both are common stock indices used to determine the overall health of the economy.

Suppose a linear regression T test on ${H}_{0}: B = 1$ vs. $H_a: B ≠ 1$ gives a $p$-value of $0.498$.

The economist can conclude which of the following?

A

There is no evidence of a linear relationship between the S&P 500 and the Dow Jones Industrial Average.

B

Insufficient evidence exists of a direct linear relationship between returns of the S&P 500 and the Dow Jones Industrial Average.

C

There is strong evidence of a linear relationship between returns of the S&P 500 and the Dow Jones Industrial Average.

D

A year of positive gains for the Dow Jones Industrial Average has nothing to do with a year of positive gains for the S&P 500.

E

There is insufficient information to provide any reasonable conclusions.

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