Respuesta :
Answer:
The endpoints of a t-distribution with 1% beyond them in each tail if the sample has size n=20 is ±2.539
Step-by-step explanation:
Consider the provided information.
It is given that the value of n = 20.
Calculate the degree of freedom as shown below:
[tex]df=n-1[/tex]
[tex]df=20-1[/tex]
[tex]df=19[/tex]
It is given that t-distribution with 1% beyond them in each tail.
Therefore the value of α = 0.01
Now use the t distribution table to find the critical value with α = 0.01 and degree of freedom 19.
The critical value with α = 0.01 and df = 19 is ±2.539
Hence, the endpoints of a t-distribution with 1% beyond them in each tail if the sample has size n=20 is ±2.539
Using the t-distribution, it is found that t = 2.861.
The endpoints are found at the critical level for a two-tailed confidence interval with a confidence level of 1 - 0.01 = 0.99.
- The number of degrees of freedom is the sample size subtracted by 1, thus, df = 20 - 1 = 19.
Looking at the t-table, with 19df (y-axis) and a confidence level of [tex]1 - \frac{1 - 0.99}{2} = 0.995[/tex]. So we have t = 2.861.
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