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Belief in Santa Claus

APSTAT-F3P1EL

A researcher wants to study the difference between $6$-year-old boys’ and girls’ belief in Santa Claus.

She asks $18$ randomly selected boys and $18$ randomly selected girls. Of those, $9$ boys and $13$ girls said they believe in Santa Claus.

The $95\%$ confidence interval for the difference in the response rates for the boys and girls was $-0.532$ to $0.088$ (boys to girls).

What can be inferred from this result?

A

It is highly likely that the same proportion of $6$-year-old boys and $6$-year-old girls believe in Santa Claus.

B

A significantly greater proportion of $6$-year-old girls believes in Santa Claus than do $6$-year-old boys.

C

No inference can be made because the sample sizes are much too small.

D

We cannot conclude that the proportion of $6$-year-old girls who believe in Santa Claus is different from the proportion of 6-year-old boys who believe in Santa Claus.

E

No inference can be made because this is a confidence interval, not a hypothesis test.