Question

In a city, 45% of the bus riders with a monthly pass are students. In a random sample of 50 bus riders with monthly passes, 18 are students.

What is ρ and ρˆ ?

ρ=0.45, ρˆ=0.18


ρ=0.45, ρˆ=0.36


ρ=0.18, ρˆ=0.45


ρ=0.36, ρˆ=0.45

Answer 1

ρ =45% or 0.45

ρ with ^ =
`(18)/(50) =0.36` or equivalently 36%

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 ^ =
`(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, 18 are students.

Using the above formula and the values given we have;

ρ with ^ =
`(18)/(50) =0.36` or equivalently 36%