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 the attendees. he found that 29 of the 63 attendees in this sample were children. among the 940 attendees at that match, 390 were children. for the facilities managers sample, find and write with proper notation the population proportion and sample proportion of attendees who were children. write the proportions as decimals (not percentages) rounded to two decimal places. (a) population proportion: select = (b) sample proportion: select =

Explanation:

Step1: Define population proportion formula

The population proportion $p$ is the proportion of children in the entire population of attendees. The formula is $p=\frac{\text{Number of children in population}}{\text{Total number of attendees in population}}$.

Step2: Calculate population proportion

We know that the number of children in the population is 390 and the total number of attendees in the population is 940. So $p = \frac{390}{940}\approx0.41$.

Step3: Define sample - proportion formula

The sample proportion $\hat{p}$ is the proportion of children in the sample. The formula is $\hat{p}=\frac{\text{Number of children in sample}}{\text{Total number of attendees in sample}}$.

Step4: Calculate sample proportion

We know that the number of children in the sample is 29 and the total number of attendees in the sample is 63. So $\hat{p}=\frac{29}{63}\approx0.46$.

Answer:

(a) Population proportion: $p = 0.41$
(b) Sample proportion: $\hat{p}=0.46$