Question

Describe the sampling distribution of x, the sample mean fill volume, for a random sample

Answer 1

Answer:

We already know how to find parameters that describe a population, like mean, variance, and standard deviation. But we also know that finding these values for a population can be difficult or impossible, because it’s not usually easy to collect data for every single subject in a large population.

We already know how to find parameters that describe a population, like mean, variance, and standard deviation. But we also know that finding these values for a population can be difficult or impossible, because it’s not usually easy to collect data for every single subject in a large population.So, instead of collecting data for the entire population, we choose a subset of the population and call it a “sample.” We say that the larger population has NN subjects, but the smaller sample has nn subjects

the same way that we’d find parameters for the population, we can find statistics for the sample. Then, based on the statistic for the sample, we can infer that the corresponding parameter for the population might be similar to the corresponding statistic from the sample.

Sampling distribution of the sample mean

Sampling distribution of the sample meanConsider the fact though that pulling one sample from a population could produce a statistic that isn’t a good estimator of the corresponding population parameter.

Sampling distribution of the sample meanConsider the fact though that pulling one sample from a population could produce a statistic that isn’t a good estimator of the corresponding population parameter.For example, maybe the mean height of girls in your class in 6565 inches. Let’s say there are 3030 girls in your class, and you take a sample of 33 of them. If you happened to pick the three tallest girls, then the mean of your sample will not be a good estimate of the mean of the population, because the mean height from your sample will be significantly higher than the mean height of the population. Similarly, if you instead just happened to choose the three shortest girls for your sample, your sample mean would be much lower than the actual population mean.