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 Jessica’s 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. 52644, 52348, 82462, 66233. 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

Answer 1

Using the given random number sequence to simulate whether students tried out for sports, we count the digits 0-3 to see how many students this represents. The proportion of these in the first 20 digits indicates that 40% of the simulated sample tried out for sports, matching the reported statistic.

Step-by-step explanation:

The question asks to use a line of random numbers to simulate whether or not students have tried out for a sport at a school, based on the reported statistic that 40% have done so. The digits 0-3 represent students who have tried out, while digits 4-9 represent those who have not. We are provided with a string of random numbers (52644, 52348, 82462, 66233) and use these to run one simulation for a sample of 20 students.

1. Count the number of digits from 0-3 in the given random numbers sequence.
2. Calculate the proportion of these digits compared to the total number of digits representing the full sample size which is 20.

Simulation results using the given numbers:

• First 20 digits: 52644523488246266233
• Count of digits representing students who tried out: 8 (since there are 8 digits within 0-3 range).
• Proportion of students who tried out in the simulation: 8/20 = 0.40.

The simulation result of 0.40 means that in our simulated sample, 40% of students have tried out for a sport which matches the reported statistic.