A simple random sample is drawn from a normally distributed population. The value of which of the following will not be known for certain but can be inferred?
Sample mean and population mean are the same for normal distributions.
To determine which value will not be known for certain but can be inferred from a simple random sample drawn from a normally distributed population, we need to understand the concept of parameter and statistic.
In statistics, a parameter is a numerical value that describes a population, while a statistic is a numerical value that describes a sample. The key difference is that a parameter is generally unknown and estimated based on sample statistics.
In this case, since we are drawing a simple random sample from a normally distributed population, the population parameter that will not be known for certain but can be inferred is the population mean (μ).
When we collect a sample, we can estimate the population mean by calculating the sample mean (x̄). The sample mean is a statistic that provides an estimate of the population mean.
Other values, such as the sample variance, sample standard deviation, or sample proportions, can also be estimated from the sample and used to make inferences about the corresponding population parameters.
However, it is important to note that while we can make inferences about the population parameter based on the sample statistics, these inferences are subject to uncertainty due to sampling variability. Therefore, although we can make an educated guess about the population mean based on the sample mean, we cannot know it for certain without examining the entire population.