Answer:
ρ =45% or 0.45
ρ with ^ = [tex]\frac{18}{50} =0.36[/tex] or equivalently 36%
Step-by-step explanation:
ρ represents the population proportion of the bus riders, with a monthly pass, who are students.
The population proportion is simply the percentage of the entire population with a particular characteristic. We have been informed that in a city, 45% of the bus riders with a monthly pass are students. This means that 45% of the whole population of bus riders with a monthly pass are students. Therefore, our ρ is simply 45% or 0.45.
ρ with ^ represents the sample proportion of the bus riders, with a monthly pass, who are students. This is a statistic or an estimator as it is normally used to estimate the value of ρ, the population proportion. It is calculated using the formula;
ρ with ^ = [tex]\frac{x}{n}[/tex]
where n represents the size of the sample and x the number of individuals in the sample with a certain desired characteristic. We have been informed that;
in a random sample of 50 bus riders with monthly passes, 18 are students.
Using the above formula and the values given we have;
ρ with ^ = [tex]\frac{18}{50} =0.36[/tex] or equivalently 36%
