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Jackie recently read a report claiming that $43.8\%$ of smartphone users have an Apple iPhone, $39.6\%$ have an Android device, $13.6\%$ have a Blackberry, and $3\%$ have some other type of smartphone. She wonders whether this distribution is true for students at her high school.

To gather data, she randomly surveyed $30\text{ students}$ who have smartphones. She found that $15$ of them have Apple iPhones, $11$ have an Android device, $3$ have a Blackberry, and $1$ has some other type of smartphone.

Does this provide evidence that the distribution of smartphones at this high school is not the same as was stated in the report?

A

Yes. $50\%$ of those surveyed had iPhones and this is far greater than the percentage stated in the report.

B

Yes. None of the observed counts from the survey match what would be expected if the percentages stated in the report are true for students at this school.

C

No. The $p$-value for the one-proportion $z$-test is too large for us to be able to conclude that the proportions stated in the report are not correct.

D

No. The $p$-value from the ${ \chi }^{ 2 }$ Goodness of Fit test is too large to provide evidence that the distribution is different from what was reported.

E

An appropriate significance test cannot be conducted in this situation, since not all conditions are satisfied.

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