Question

Which of the following is NOT the component of the confidence intervals for the population mean?

a) Standard Error
b) population mean
c) sample size
d) sample mean

Answer 1

The population mean is NOT a component of the confidence intervals for the population mean; instead, confidence intervals are constructed using the sample mean, standard error, and sample size to estimate the population mean.

Step-by-step explanation:

The component that is NOT a part of the confidence intervals for the population mean is b) population mean. When constructing a confidence interval for a population mean, we use the sample mean, the standard error of the mean, and the sample size to estimate the range within which we believe the population mean lies. These components are used to calculate the error bound around the sample mean, thereby creating an interval that we are a certain percent confident contains the true population mean. The population mean itself is not a part of the interval; instead, it is the parameter that the interval is trying to estimate.

The standard error is calculated from the sample standard deviation and the sample size. The sample mean is the average of the values in the sample, used as the point estimate for the population mean. Sample size affects the width of the confidence interval; a larger sample size tends to produce a narrower interval, indicating a more precise estimate.

Answer 2

The correct answer is b) population mean, as the population mean is not a component of the confidence interval; the confidence interval is constructed to estimate this unknown parameter.

The correct answer is B.

Step-by-step explanation:

The question is asking which of the listed options is NOT a component of the confidence intervals for the population mean. A confidence interval for a population mean typically includes three primary components: the sample mean (x), the standard error of the mean (which accounts for both the sample standard deviation (s) and the sample size (n)), and the critical value from the specified distribution (Z or t-score), which is based upon the desired confidence level. The population mean (μ) is not a component of a confidence interval because the confidence interval is an estimate of where this unknown parameter μ is likely to lie.

To construct a confidence interval, one would typically use the following formula:

• x ± (critical value) * (standard error)

Standard error is calculated from the sample data and is defined as the sample standard deviation divided by the square root of the sample size.

Therefore, the correct answer to the question "Which of the following is NOT the component of the confidence intervals for the population mean?" is b) population mean.