Question

jordyn collects data on students in her school district who play in the school band. she chooses two random samples, each containing 50 students. the table shows her data. based on the data, complete the estimation about the population. about 60% of the students who play in a school band are 7th graders. there are 400 students in the school district who play in a school band. which is the best estimate of the number of 7th graders in the district who play in a school band? 35 95 120 240

Explanation:

Step1: Calculate the proportion of 7th - graders in each sample

• For Sample 1: The number of 7th - graders is \(26\), and the sample size is \(50\). The proportion \(p_1=\frac{26}{50}=0.52\)
• For Sample 2: The number of 7th - graders is \(34\), and the sample size is \(50\). The proportion \(p_2=\frac{34}{50} = 0.68\)
• The average proportion of 7th - graders in the two samples is \(\frac{0.52 + 0.68}{2}=\frac{1.2}{2}=0.6\) (which is \(60\%\) as given in the problem)

Step2: Use the proportion to estimate the number of 7th - graders in the population

If the proportion of 7th - graders in the sample is \(p = 0.6\) (or \(60\%\)) and the population size \(N=400\)
The estimated number of 7th - graders \(n=p\times N\)
Substitute \(p = 0.6\) and \(N = 400\) into the formula: \(n=0.6\times400=240\)

Answer:

\(240\)