Question

1. look again at the graph above that is displaying the results of 38 simple random samples. if each student had taken a larger sample of size 20 words instead of a smaller sample of size 5 words, how would you expect the graph to change? please explain.

Explanation:

When sample size increases (from 5 to 20 words), the sampling distribution becomes more concentrated around the true population parameter (due to the Central Limit Theorem and the fact that larger samples have less sampling variability). So the graph's data points (sample statistics) would be less spread out (smaller range, less variability), and the distribution would be more clustered, likely closer to the true value, with a narrower spread (e.g., smaller standard deviation of the sample statistics). Also, the shape might become more symmetric and bell - shaped (if applicable) as sample size increases, approaching a normal distribution more closely.

Answer:

When the sample size increases from 5 to 20 words, we would expect the graph (of sample statistics) to show less variability (a narrower spread, e.g., smaller range or standard deviation of the sample - related values). The data points (sample statistics) would be more clustered around the true population parameter. This is because larger samples have less sampling variability: as sample size \(n\) increases, the standard error (a measure of sampling variability, e.g., \(\frac{\sigma}{\sqrt{n}}\) for the mean) decreases, so sample statistics are more likely to be close to the true population value, leading to a more concentrated distribution of the sample - based results in the graph.