For basic questions in statistics involving the properties or use of standard error of the sample points present in a simple random sample.

The standard deviation of the sampling distribution of a statistic is called the standard error.

For basic questions in statistics involving the properties or use of standard error of the sample points present in a simple random sample.

The standard deviation of the sampling distribution of a statistic is called the standard error.

95 questions

votes

When you divide in hypothesis testing you use the formula:
$$
\frac{\bar X-\mu}{s/\sqrt n}
$$
but the standard error of the mean is:
$$
\frac s{\sqrt {n-1}}
$$
Why don't you use $n-1$ when calculating the standard error using the sample population?

Rob

- 197
- 1
- 7

votes

I've been studying descriptive statistics and am having a hard time understanding the actual intuition behind standard deviation. I'm trying to get a practical feeling for it and so I'm trying to draw conclusions from it using a distribution of 20…

Danilo Souza Morães

- 185
- 6

votes

I would like to ask for the interpretation, both mathematically and intuitively if possible, about the homoscedasticity of the variance of errors in linear regression models.
If there is correlation among the error terms, then how it would affect…

Sophil

- 365
- 3
- 10

votes

When input quantities contain uncertainty, how those uncertainties are propagated to the output for operations of addition, subtraction, multiplication and division can be found in literature defined using various rules.
However for bitwise…

hpd

- 111
- 3

votes

I have accrossed the below integral when i have tried to know more about relationship between error function and CDF of the normal distribution ,I plug this integral in wolfram alpha but no result , but some of my weaker gaven assure that is…

zeraoulia rafik

- 6,570
- 1
- 18
- 51

votes

To calculate the random error in a set of measurements this is what I would do.
Get the standard deviation of the measurements:
$$ \sigma=\sqrt{\frac{1}{N-1}\Sigma_{i=1}^N(x_i-\bar{x})^2} $$
Where $N$ is the number of repeats, $x_i$ is the value…

Mathsie

- 31
- 6

votes

I have a collection of data points. I have computed the histogram of this data to create the empirical distribution. How can estimated the error in the value at each bin. Based on the the total number of data points and the counts at each bin.
The…

Jared Lo

- 157
- 1
- 7

votes

We have a 90%-confidence interval. I want to check if the following statements are correct.
If double the sample, the possibility that the value that we are looking for is out of the confidence interval is smaller.
The bigger the standard error,…

Mary Star

- 12,214
- 10
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- 149

votes

I am trying to derive the following formula given by the lecture notes
$$SE(\hat{\beta_0}+\hat{\beta_1}x_0)=\hat{\sigma}\bigg[\frac{1}{n}+\frac{(x_0-\bar{x})^2}{(n-1)s^2_x}\bigg]^\frac{1}{2}$$
My…

LJNG

- 779
- 2
- 11

votes

Question: Suppose that $X$ is a discrete random variable with :
\begin{array}{|r|r|r|r|}
\hline
X & 0 & 1 & 2 & 3\\ \hline
\mathbb P(X=x) &\frac{2}{3}\theta &\frac{1}{3}\theta &\frac{2}{3}(1-\theta) &\frac{1}{3}(1-\theta)…

falamiw

- 441
- 2
- 13

votes

Given a multiple regression with the usual assumptions satisfied, with $X \in R^{n \times p}$
$$ y = X \beta + e $$
I know that the estimated variance is given by $\sigma^2 (X^TX)^{-1}$. But what I want to know is the estimated variance for the…

Jay

- 205
- 2
- 8

votes

Sorry, I'm just on Khan academy and can't seem to grasp the essence of statistics. Hope to find some help out here.
Both are samples, but why when looking for confidence interval of a:
sample proportion, we take $\hat{p} \pm…

nvs0000

- 643
- 2
- 7

votes

When drawing a sample of size n from population of size N
This relationship holds
$$ SE\space when\space drawing\space sample\space without\space replacement\space =\space correction\space factor\space *\space SE\space when\space …

q126y

- 499
- 5
- 17

votes

Using Stirling's formula, how can we bound the absolute error of $$e^x-\sum_{n=0}^N \frac{x^n}{n!}$$ on the interval $|x|\leq R$ where $R\leq N/2e$

user19289

- 167
- 1
- 8

votes

I understand standard error and confidence intervals as formulas, but not as concepts. Can you help me understand them better?
A smaller standard deviation (smaller spread of your data) and a larger sample size both give you a smaller standard…

Michael Cornn

- 135
- 3