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Police stops ~ The Minneapolis Police Department records data on all traffic stops made by their...

Police stops ~ The Minneapolis Police Department records data on all traffic stops made by their police officers such as race, gender, reason, citation issued, etc. To estimate the proportion of female drivers who are stopped, the chief of police takes a random sample of 100 traffic stops and finds that in 20 of them, the driver was female. Using this data, the chief of police wants to estimate the actual proportion of drivers who are stopped that are female.

We want to use statistical inference to estimate the actual proportion of drivers who are stopped that are female.


To use a normal distribution in this scenario, which of the following conditions must be satisfied?

Question 12 options:

Any two samples must be independent of each other.

There must be at least 10 observed successes and 10 observed failures in the sample.

Both n×p0 and n×(1−p0)must be at least 10 where p0 is the null value for the population proportion.

The observations within the sample must be independent of each other.

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Answer #1

The sampling distribution for ^p, taken from a sample of size n from a population with a true proportion p, is nearly normal when

1. the sample observations are independent and

2. we expected to see at least 10 successes and 10 failures in our sample

3. np >10 and n(1 - p) > 10. This is called the success-failure condition.

If these conditions are met, then the sampling distribution of ^p is nearly normal with mean p and standard error.

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