Respuesta :
Answer:
Standard error = 0.01029
Step-by-step explanation:
Data provided in the question:
Sample size, n = 5
prices: 1.93, 1.97, 1.99, 1.96, 1.98,
Now,
The standard error is calculated using the formula :
Standard error = [tex]\sqrt{\frac{\sigma^2}{n}}[/tex]
Here,
σ² is the variance
Mean = [tex]\frac{\textup{ 1.93 + 1.97 + 1.99 + 1.96 + 1.98}}{\textup{5}}[/tex]
= 1.966
Data Data - Mean (Data - Mean)²
1.93 -0.036 0.001296
1.97 0.004 0.000016
1.99 0.024 0.000576
1.96 -0.006 0.000036
1.98 0.014 0.000196
=================================
∑(Data - Mean)² = 0.00212
thus,
Variance, σ² = [tex]\frac{\sum\textup{(Data-Mean)}^2}{\textup{n-1}}[/tex]
or
Variance, σ² = [tex]\frac{0.00212}{\textup{5-1}}[/tex]
or
Variance, σ² = 0.00053
Therefore,
Standard error = [tex]\sqrt{\frac{0.00053}{5}}[/tex]
or
Standard error = √0.000106
or
Standard error = 0.01029
Finding the sample standard deviation and dividing by the sample size, it is found that the standard error of the sample mean is of 0.0103.
- The sample standard deviation is the square root of the sum of the differences squared of each observation and the mean, divided by the one less than the number of values.
- The sample mean is the sum of all values divided by the number of values.
The values are: 1.93, 1.97, 1.99, 1.96, 1.98.
The sample mean is:
[tex]\overline{x} = \frac{1.93 + 1.97 + 1.99 + 1.96 + 1.98}{5} = 1.966[/tex]
The sample standard deviation is:
[tex]s = \sqrt{\frac{(1.93-1.966)^2+(1.97-1.966)^2+(1.99-1.966)^2+(1.96-1.966)^2+(1.98-1.966)^2}{4}} = 0.0230[/tex]
The standard error is:
[tex]S_e = \frac{s}{\sqrt{n}} = \frac{0.0230}{\sqrt{5}} = 0.0103[/tex]
The standard error is of 0.0103.
A similar problem is given at https://brainly.com/question/22718960
