Question

the gazelles are a professional soccer team based in a large city. at the teams home matches, childrens admission is half - off. at the last home match, the facilities manager took a sample of 94 attendees. he found that 49 of these attendees were children. at that match, 27 out of every 63 attendees were children. for the facilities managers sample, find and write with proper notation the sample proportion and population proportion of attendees who were children. write the proportions as decimals (not percentages) rounded to two decimal places. (a) sample proportion: select = (b) population proportion: select =

Explanation:

Step1: Calculate the sample proportion

The sample proportion \( \hat{p} \) is calculated as the number of children in the sample divided by the sample size.
The formula is \( \hat{p}=\frac{x}{n} \), where \( x = 49 \) (number of children in the sample) and \( n = 94 \) (sample size).
So, \( \hat{p}=\frac{49}{94}\approx0.52 \)

Step2: Calculate the population proportion

The population proportion \( p \) is calculated as the number of children in the population divided by the population size.
The formula is \( p=\frac{a}{b} \), where \( a = 27 \) (number of children in the population) and \( b = 63 \) (population size).
So, \( p=\frac{27}{63}=\frac{3}{7}\approx0.43 \)

Answer:

(a) Sample proportion: \( \hat{p}=0.52 \)
(b) Population proportion: \( p = 0.43 \)