Respuesta :
Answer:
1. Option B) N(μ, σ/√n)
2. Option A) a parameter
Step-by-step explanation:
We are given the following information in the question:
A simple random sample is drawn from a large population with a Normal distribution.
Since sampling is done, we have to consider standard error caused due to sampling.
[tex]\text{Standard error} = \displaystyle\frac{\text{Standard deviation}}{\sqrt{\text{Sample size}}} = \frac{\sigma}{\sqrt{n}}[/tex]
Thus, the sampling distribution of the sample mean is
Option B) N(μ, σ/√n)
- A confidence interval is an interval constructed around a point estimate.
- A confidence interval indicates how sure are we that the interval contains the population parameter.
Thus, a confidence interval is constructed to estimate the value of a parameter.
Option A) a parameter
The sampling distribution of the sample mean is N(μ. σ/ √n). A confidence interval is constructed to estimate the value of a parameter.
From the given information;
Mean [tex]\mathbf{\mu}[/tex] of the sample which is the average of all values in the sample.
where;
- The standard deviation = [tex]\mathbf{\sigma}[/tex]
- The sample size = n
The sample distribution of the above sample mean can be computed as:
[tex]\mathbf{\mu_{\bar{x}} = \mu}[/tex]
Also, the sampling distribution of the standard deviation is also expressed as:
[tex]\mathbf{\sigma_{\bar{x}} = \dfrac{\sigma}{\sqrt{n}}}[/tex]
∴
For a Normal distribution (N), the sampling distribution of the sample mean can be expressed as:
[tex]\mathbf{=N \Big(\mu, \dfrac{\sigma }{\sqrt{n}}\Big)}[/tex]
Option B is correct.
The confidence interval level is usually used to estimate or determine the population parameter of the mean or population proportion.
Therefore, we can conclude that the confidence interval is constructed to estimate the value of a parameter.
Learn more about sample mean here:
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