Question

Knowing the population standard deviation, a 95% confidence interval infers that the population mean ___________. is between 0 and 100% is within ±1.96 standard deviations of the sample mean is within ±1.96 standard errors of the sample mean is too large

Answer 1

Answer:

within ±1.96 standard deviations of the sample mean

Step-by-step explanation:

A 95% confidence interval is found using the formula C = 1 - α, and some other stuff, but let's focus on that for now. Using the formula:

.95 = 1 - α

α = .05

If α = .05, that means a 2-sided confidence interval would be found using the sample mean and the Z-score Z(subscript α/2), or Z.₀₂₅ because α AKA .05 divided by 2 = .025. From there, you take this either to your calculator or a Z-table (or perhaps you have a chart that lists the common CI values), and see that for the area to be .025 beneath a standard normal curve, your Z value is ±1.96 ("plus or minus" because we're considering a 2-sided confidence interval).

Answer 2

Using the z-distribution, it is found that the correct statement is:

• Knowing the population standard deviation, a 95% confidence interval infers that the population mean within ±1.96 standard errors of the sample mean.

Z-distribution interval

• When the population standard deviation is known, the z-distribution is used.

• The interval is given by:

$\overline{x} \pm z\frac{\sigma}{\sqrt{n}}$

In which:

• $\overline{x}$ is the sample mean.  

• $\sigma$ is the standard deviation of the sample.

• n is the sample size.

• z is the critical value.

Using a z-distribution calculator, it is found that the critical value for a 95% confidence interval is z = 1.96, which means that the population mean is within ±1.96 standard errors of the sample mean.

To learn more about the use of the z-distribution for confidence intervals, you can take a look at https://brainly.com/question/25779801