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?
mean
A simple random sample is a representative subset of a population that is drawn in such a way that each member of the population has an equal chance of being included in the sample. When a simple random sample is drawn from a normally distributed population, certain characteristics of the population can be inferred with a certain level of confidence.
In the context of your question, there are certain characteristics that can be inferred from a simple random sample drawn from a normally distributed population. These include:
1. Population mean: The mean of the population can be estimated by calculating the sample mean and considering it as an estimate of the population mean. The sample mean provides an unbiased estimate of the population mean.
2. Population variability: The sample standard deviation can be used as an estimate of the population standard deviation. This gives an indication of how spread out the values are in the population.
3. Confidence intervals: By calculating the sample mean and sample standard deviation, along with the sample size, it is possible to construct confidence intervals. These intervals provide a range within which the population mean is likely to fall given a certain level of confidence.
4. Population distribution: By examining the distribution of the sample data, it is possible to make inferences about the distribution of the population. If the sample data follow a normal distribution, it can be inferred that the population has a normal distribution.
Now, considering the options you provided, the value of the population mean is something that can be inferred with a certain level of confidence from a simple random sample drawn from a normally distributed population. The sample mean provides an estimate of the population mean. Therefore, the value of the population mean is not known for certain but can be inferred.