The value needed to determine a confidence interval for a sample mean is the standard error of the mean option (D) is correct.
What is a confidence interval for population standard deviation?
It is defined as the sampling distribution following an approximately normal distribution for known standard deviation.
The formula for finding the confidence interval for population standard deviation as follows:
[tex]\rm s\sqrt{\dfrac{n-1}{\chi^2_{\alpha/2, \ n-1}}} < \sigma < s\sqrt{\dfrac{n-1}{\chi^2_{1-\alpha/2, \ n-1}}}[/tex]
Where s is the standard deviation.
n is the sample size.
[tex]\chi^2_{\alpha/2, \ n-1} and \chi^2_{1-\alpha/2, \ n-1}[/tex] are the constant based on the Chi-Square distribution table:
α is the significance level.
σ is the confidence interval for population standard deviation.
Calculating the confidence interval for population standard deviation:
We know significance level = 1 - confidence level
It is given that:
The value needed to determine a confidence interval for a sample mean is the standard error of the mean.
CI = X + Z(s/√n)
Here CI is the confidence interval
Z is the confidence level
X is the sample mean
Thus, the value needed to determine a confidence interval for a sample mean is the standard error of the mean option (D) is correct.
Learn more about the confidence interval here:
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