Question

A class of 20 seventh graders wants to estimate the proportion of middle school students who play a sport outside of school. Each member of the class took a random sample of 10 middle school students and asked each student if he or she plays a sport outside of school. The dot plot represents the sample proportions.

What is a reasonable estimate for the proportion of all middle school students who play a sport outside of school?
Responses
0.3
0.4
0.5
0.6

Answer 1

To estimate the proportion of all middle school students who play a sport outside of school based on the dot plot of sample proportions taken by the seventh graders, we need to analyze the data represented in the plot.

Without seeing the actual dot plot, a general approach to estimating the proportion involves looking for the central tendency of the samples collected. Typically, you may consider the median or the average of the provided sample proportions.

If the proportions in the dot plot are spread around a certain value, that might indicate where the true population proportion lies. Since common estimates typically range from 0.3 to 0.6 in middle school sport participation, you would analyze where the majority of the dots cluster.

Assuming the sample proportions are reasonably distributed around a central value to give us a starting point, a good estimate could be one of the mid-range options like 0.4 or 0.5.

Given this reasoning, without specific information from the dot plot, if we must choose an option, I would suggest that **0.4** is often a safe estimate for proportions around sports participation among middle schoolers, but if the plot is heavily skewed or centered around 0.5, then that would be a better choice.

**Final suggestion:** Based on typical participation rates, **0.4** or **0.5** would likely be reasonable estimates, with 0.4 being slightly conservative. So if you're forced to pick one, **0.4** is a reasonable estimate if the data doesn't heavily show otherwise.