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A spokesman for a large cereal company is interested in whether a new promotion of including a toy in every box of cereal would greatly increase sales.

He figures that age would be a factor, so he selects one pair of subjects at each age range from $10$ to $79$ by increments of $5$ years.

The spokesman flips a coin to decide which of the pair gets a coupon for a free prize every time they buy a box of the cereal. After one year, each subject is asked how many boxes of that brand of cereal they bought. The data is in the table below:

Age Range 10- 14 15- 19 20- 24 24- 29 30- 34 35- 39 40- 44 45- 49 50- 54 55- 59 60- 64 65- 69 70- 74
With Coupon 9 8 8 5 4 12 14 13 8 6 5 4 4
Without Coupon 7 4 8 6 5 7 8 7 6 6 4 3 4

From this data, is there convincing statistical evidence that people buy more cereal when a prize coupon is included?

A

Yes, at the $1\%$, $5\%$, and $10\%$ alpha levels.

B

Yes, at the $5\%$ and $10\%$ alpha level, but not the $1\%$ level.

C

Yes, at the $10\%$ alpha level, but not the $5\%$ or $1\%$ levels.

D

No, not at none of the common alpha levels of $1\%$, $5\%$, or $10\%$.

E

Yes, since the mean of the “with prize” is above the mean of the “without prize.”

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