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Fantasy football consists of a competition where participants select players from different football teams and points are awarded based on the performance of those players. A student was curious if the fantasy football totals for quarterbacks from the first $3\text{ weeks}$ of the season was a good indicator of how well these players would do the rest of the season.

The student measured the performances of $21$ starting quarterbacks and ran a 2 sample $T$-test to determine if the number of fantasy football points in the first $3\text{ weeks}$ of the season differed from the fantasy football points the rest of the year.

After running a two-sided test, a $P$-value of $6.83\%$ was calculated.

How might you interpret the $P$-value in the context of the problem?

A

$6.83\%$ of quarterbacks have lower averages the rest of the season compared to the first three weeks.

B

If there were really no difference between an NFL quarterback’s performance during the first three weeks and their performance the rest of the season, getting differences of this size or greater would be somewhat unlikely (in fact, about $6.83\%$).

C

Approximately $6.83\%$ of quarterbacks in this sample had higher average fantasy points for the remainder of the season compared to the first three weeks.

D

There is approximately a $6.83\%$ chance of this data occurring.

E

There is approximately a $6.83\%$ chance of getting a difference such as this, or less,in this sample, by chance alone.

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