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Joe is an early bird. He is up at the crack of dawn and ready to begin his day! His sister, Eve, however, is a night owl. She is awake and active well into the night, but hates getting up the next morning.

Joe and Eve started to wonder whether gender has anything to do with preferences for morning or night. To investigate, they interviewed a random sample of individuals and asked them to identify themselves as being either more of an early bird or more of a night owl. The results of their survey are organized into the two-way table below:

Early Bird Night Owl
Male 48 46
Female 47 53

If gender and preference for time of day are independent, which of the following statements is most likely not true?

A

A ${\chi}^{2}$ test for association will return a $p$-value that is statistically insignificant.

B

A $2$-sample $z$-test for a difference in the proportion of female night owls vs. the proportion of male night owls will return a $p$-value that is statistically insignificant.

C

The expected count for males who are early birds is $46.03$.

D

The expected count for females who are night owls is greater than the actual count of females who said they were more of a night owl.

E

If a surveyed individual said they were more of an early bird, the probability that the individual was male is $\frac{47}{97}$.

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