I have a question about t-statistics in first place I need to use t-statistics to estimate the population mean from a sample set, as you see I have a data set the mean and standard deviation are known for sample but not for the population. How can I use t-statistics to determine the population mean I have X bar and S and n values for sample n=45 how can I compute the degree of freedom and how can I determine the confidence level? thanks for your time huge regards

Amiya Melendez

Amiya Melendez

Answered question

2022-10-20

I have a question about t-statistics in first place I need to use t-statistics to estimate the population mean from a sample set, as you see I have a data set the mean and standard deviation are known for sample but not for the population.
How can I use t-statistics to determine the population mean I have X bar and S and n values for sample n = 45how can I compute the degree of freedom and how can I determine the confidence level? thanks for your time huge regards

Answer & Explanation

periasemdy

periasemdy

Beginner2022-10-21Added 15 answers

Step 1
d f = n 1
You need to set the confidence level yourself. α = .05 is standard.
Confidence interval:
U p p e r l i m i t = X b a r + t q u a n t i l e ( 1 α / 2 , d f ) S d f
L o w e r l i m i t = X b a r t q u a n t i l e ( 1 α / 2 , d f ) S d f
Step 2
Where tquantile is the quantile from a t-distribution chart or obtained from statistical software. It is 2.015368 so you have:
U p p e r l i m i t = X b a r + 2.015368 S d f
L o w e r l i m i t = X b a r 2.015368 S d f
In R:
> qt(.975,44)
[1] 2.015368

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