The manager of Lawn and Garden Services would like to estimate the proportion of her employees' time spent performing various gardening and lawn care activities. She has made 400 random observations of a typical worker, with the following results: $$\begin{array} { l c }
\text { Activity } & \text { Time Observed } \
\hline \text { Mowing } & 200 \
\text { Trimming } & 80 \
\text { Raking } & 40 \
\text { Miscellaneous } & 80
\end{array}$$ What is the probability that the true proportion of time spent mowing is exactly equal to the sample proportion?
A) 0
B) .1
C) .2
D) .5
E) 1

Question

The manager of Lawn and Garden Services would like to estimate the proportion of her employees' time spent performing various gardening and lawn care activities. She has made 400 random observations of a typical worker, with the following results: $$\begin{array} { l c } 
\text { Activity } & \text { Time Observed } \
\hline \text { Mowing } & 200 \
\text { Trimming } & 80 \
\text { Raking } & 40 \
\text { Miscellaneous } & 80
\end{array}$$ What is the probability that the true proportion of time spent mowing is exactly equal to the sample proportion?
A) 0
B) .1
C) .2
D) .5
E) 1

Quizplus · Accepted Answer

It is not possible for the true proportion of time spent mowing to be exactly equal to the sample proportion, because the sample proportion is a specific value obtained from the 400 observations, and the true proportion is an unknown parameter that represents the proportion of all employees' time spent mowing. These two values may be close to each other, but they are not expected to be exactly equal. Therefore, the probability of their exact equality is zero.

The Manager of Lawn and Garden Services Would Like to Estimate