Importance of Population Standard Deviation in Creating Confidence Intervals for Population Mean

Which of the following statements correctly describe the role of the population standard deviation, σ, in creating a confidence interval for the population mean? Select all that apply.

To create a confidence interval for the population mean, the population standard deviation, σ, plays a crucial role

To create a confidence interval for the population mean, the population standard deviation, σ, plays a crucial role. The correct statements that describe its role are:

1. The population standard deviation, σ, provides a measure of the variability or spread of the data values in the population. It helps in understanding how much the individual data points differ from the mean.

2. The population standard deviation, σ, is used in the calculation of the standard error of the mean (SE). The standard error represents the average deviation of the sample means from the true population mean.

3. The population standard deviation, σ, directly affects the width of the confidence interval. A larger standard deviation leads to a wider confidence interval, indicating more uncertainty about the true population mean.

4. The population standard deviation, σ, is usually unknown and needs to be estimated from the sample data. This estimation is done by calculating the sample standard deviation, s, which is then used as a substitute for σ in the confidence interval formula.

It is important to note that the population standard deviation is not always known, which is why the sample standard deviation is used as an estimate. However, if the population standard deviation is known, it can be directly used in the calculation of the confidence interval.

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