# Mathematics and Statistics

What proportion of students are willing to report cheating by other students? A student project put this question to an SRS of 172 undergraduates at a large university: “You witness two students cheating on a quiz. Do you go to the professor?” Only 19 answered “Yes.”

A. Show that the conditions for calculating a confidence interval for a proportion are satisfied.

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RANDOM? The data (does/does not) come from a random sample from the population of interest.

LARGE COUNTS CONDITION?

?⋅?≥10n⋅p≥10

___ ____ > 10

___> 10

?(1−?)≥10n(1−p)≥10

___(__ ) > 10

___ > 10

B. Calculate a 99% confidence interval for the proportion of all undergraduate students at this university who would answer “Yes.” Record the interval below.

to

C. Interpret the interval from Part B.

Sorry! A recent poll of 738 randomly selected customers of a major U.S. cell-phone carrier found that 170 of them had walked into something or someone while talking on a cell phone.

D. Show that the conditions for calculating a confidence interval for a proportion are satisfied.

RANDOM? The data (does/does not) come from a random sample from the population of interest. See also https://en.wikipedia.org/wiki/Mathematical_statistics for more details.

LARGE COUNTS CONDITION?

?⋅?≥10n⋅p≥10

10
10

?(1−?)≥10n(1−p)≥10

( ) > 10

10

E. Calculate a 90% confidence interval for the proportion of all customers who have walked into something or someone while talking on a cell phone. Record the interval below.

to

F. Interpret the interval from Part E.

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