Question

a study reported that about 40% of high school students have tried out for a sport at their school. to find out if this applies to jessicas school, she surveyed an srs of 20 students. nine of them said that they had tried out for a sport. to see if this result is surprising, a simulation is to be conducted to estimate the probability of obtaining a sample result as high as this one.
let 0 - 3 represent students who tried out for a sport and 4 - 9 represent students who did not try out for a sport.
using the line of random numbers to run one simulation, what proportion of students tried out for a sport?
0.40
0.45
0.50
0.60
52844 52348 82462 66233

Explanation:

Step1: Count the number of students who tried out for a sport

We are given the line of random numbers: \(52844\), \(52348\), \(82462\), \(66233\).
For each digit in these numbers:

• In \(52844\): The digits are \(5\), \(2\), \(8\), \(4\), \(4\). The digit \(2\) (where \(0 - 3\) represents tried out) is \(1\) digit that represents a student who tried out.
• In \(52348\): The digits are \(5\), \(2\), \(3\), \(4\), \(8\). The digits \(2\) and \(3\) (where \(0 - 3\) represents tried out) are \(2\) digits that represent students who tried out.
• In \(82462\): The digits are \(8\), \(2\), \(4\), \(6\), \(2\). The digits \(2\) and \(2\) (where \(0 - 3\) represents tried out) are \(2\) digits that represent students who tried out.
• In \(66233\): The digits are \(6\), \(6\), \(2\), \(3\), \(3\). The digits \(2\), \(3\), \(3\) (where \(0 - 3\) represents tried out) are \(3\) digits that represent students who tried out.

The total number of digits that represent students who tried out is \(1 + 2+2 + 3=9\).

Step2: Calculate the proportion

The sample size \(n = 20\) (since we have \(4\) groups of \(5\) - digit numbers, \(4\times5=20\) digits).
The proportion \(p=\frac{\text{Number of successes (students who tried out)}}{\text{Sample size}}\)
\(p=\frac{9}{20}=0.45\)

Answer:

\(0.45\)