A sixth-grade class has 20 total students, while the entire middle school has 1,000 students. A census is taken of the entire school’s population to see on which day of the week every student was born. Theoretically, 14.3%, or 1/7 of the students should have been born on each day. The table here shows that the results for the entire school are closer to this prediction than the results for the sixth-grade class are. What is a good explanation for this?
A) The sixth-graders were all born during the same year and that year was probably an unusual, aberrant year.
B) The data for the entire school is more statistically meaningful because it is drawn from a much larger population.
C) Sixth-graders are younger than the rest of the middle school and more likely to have made errors in their data collection.
D) The data for the entire school reflects students from different grades, while the data for the sixth-grade class is only for sixth-graders.
B) The data for the entire school is more statistically meaningful because it is drawn from a much larger population.
Hey B is the answer to it
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The correct explanation for why the results for the entire school are closer to the predicted values than the results for the sixth-grade class is B) The data for the entire school is more statistically meaningful because it is drawn from a much larger population.
Here's how you can arrive at this answer:
The question states that the theoretical prediction is that 14.3%, or 1/7, of the students should have been born on each day of the week. This would only be true if the population is large enough and random.
In the case of the entire middle school, which has 1,000 students, the sample size is significantly larger compared to the sixth-grade class of only 20 students. When the sample size is larger, the data tends to be more representative and closer to the population's true characteristics. This is because a larger sample size reduces the effect of random variation, making the data more statistically meaningful.
On the other hand, the smaller sample size of the sixth-grade class leaves more room for sampling error and random variation, which can lead to results that deviate from the predicted values.
Therefore, option B is the best explanation for why the results for the entire school are closer to the predicted values than the results for the sixth-grade class.