At Brighton Middle School, Mr. Yule asked 50 randomly selected students from each grade level about their favorite subject, and 12 chose science. He used this data to draw the inference that about 25% of middle school students will indicate science is their favorite subject. If there are 200 students all together, did he make a reasonable inference? No, Mr. Yule’s sample is biased and too small to be representative of the population. Yes, Mr. Yule’s sample is small and biased, so it is representative of the population. No, Mr. Yule’s percentage is too large. He should have used 6%. Yes, Mr. Yule’s sample is random and representative of the population.

Answer

No, Mr. Yule’s sample is biased and too small to be representative of the population. Mr. Yule’s inference is based on a sample of 50 randomly selected students from each grade level, which is not enough to draw a conclusion about the entire population of 200 students. Furthermore, the sample is biased since it only includes those students willing to participate, without accounting for the others.

Random Sampling

Random sampling is the process of selecting members of a population at random in order to draw conclusions about the entire population. It is important to ensure that the sample is truly random in order to ensure that it accurately reflects the entire population.

Bias

Bias is when the sample population does not accurately reflect the entire population. In Mr. Yule’s case, the sample is only composed of students willing to participate in the survey, not the entire population of 200 students. This means that the results may not accurately reflect the true population.

Significance

Significance is the degree of certainty that can be placed on the results of a survey or experiment. In Mr. Yule’s case, the sample size of 50 students is not large enough to be considered statistically significant. Therefore, any conclusions drawn from the survey cannot be considered reliable.

Related Questions

• What is random sampling?
• What is bias?
• What is significance?
• What is the difference between bias and random sampling?
• What is the difference between bias and significance?
• What is a sample size?
• How do you ensure a sample is random?
• What is a representative sample?
• What is the difference between random sampling and representative sampling?
• How do you determine the significance of a survey?