Question

In a city, 35% of the bus riders with a monthly pass are students. in a random sample of 50 bus riders with monthly passes, 23 are students.
what is ρ and ρ with ^

Answer 1

Answer:

ρ = 35% or 0.35

ρ with ^ = $\frac{23}{50}=0.46$ or equivalently 46%

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, 35% of the bus riders with a monthly pass are students. This means that 35% of the whole population of bus riders with a monthly pass are students. Therefore, our ρ is simply 35% or 0.35.

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 ^ = $\frac{x}{n}$

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, 23 are students.

Using the above formula and the values given we have;

ρ with ^ = $\frac{23}{50}=0.46$ or equivalently 46%