Respuesta :
Answer:
For this case since the sample size is < 30 is appropiate use the t distribution.
[tex]df=n-1=12-1=11[/tex]
[tex]SE= \frac{s}{\sqrt{n}}=\frac{1.621}{\sqrt{12}}=0.468[/tex]
Step-by-step explanation:
The t distribution (Student’s t-distribution) is a "probability distribution that is used to estimate population parameters when the sample size is small (n<30) or when the population variance is unknown".
The shape of the t distribution is determined by its degrees of freedom and when the degrees of freedom increase the t distirbution becomes a normal distribution approximately.
The degrees of freedom represent "the number of independent observations in a set of data. For example if we estimate a mean score from a single sample, the number of independent observations would be equal to the sample size minus one."
Based on the info given we have these values:
5, 6, 6, 7, 7, 7, 8, 8, 8, 9, 9, 11
And for this case we have n=12 representing the sample size.
For this case since the sample size is < 30 is appropiate use the t distribution.
We can calculate the sample mean and the deviation with the following formulas:
[tex]\bar X =\frac{\sum_{i=1}^n X_i}{n}=7.583[/tex]
[tex]s=\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}=1.621[/tex]
We can calculate the degrees of freedom like this:
[tex]df=n-1=12-1=11[/tex]
And the standard error for the sample mean is given by:
[tex]SE= \frac{s}{\sqrt{n}}=\frac{1.621}{\sqrt{12}}=0.468[/tex]
The t-distribution is appropriate for a dataset
How to determine if the t-distribution is appropriate?
From the dotplot of the sample, we have the following frequency distribution
Sample Frequency
5 1
6 2
7 3
8 3
9 2
11 1
Total 12
A t-distribution is appropriate for a dataset whose sample size is less than 30.
The sample size (12) of the dot plot is less than 30.
Hence, the t-distribution is appropriate for a dataset
Read more about the t-distribution at:
https://brainly.com/question/16959076
