Question

Use the Student's t distribution to find t_{c} for a 0.95 confidence level when the sample is 24.

Confidence intervals
ANSWERED
asked 2021-08-01

Use the Student's t distribution to find \(t_{c}\) for a 0.95 confidence level when the sample is 24. (Round your answer to three decimal places.)

Answers (1)

2021-08-09
Step 1
Obtain the critical value of t using the student's t distribution to find \(\displaystyle{t}_{{{c}}}\) for a 0.95 confidence level when the sample is 24.
The critical value of t is obtained below:
From the information, given that \(\displaystyle{n}={24}\).
Obtain the degrees of freedom.
The degrees of freedom is obtained below:
\(\displaystyle{d}{f}={n}-{1}\)
\(\displaystyle={24}-{1}\)
\(\displaystyle={23}\)
Here, confidence level is 0.95.
For \(\displaystyle{\left({1}-\alpha\right)}={0.95}\)
\(\displaystyle\alpha={0.05}\)
Step 2
Use EXCEL Procedure for finding the critical value of t.
Follow the instruction to obtain the critical value of t:
1.Open EXCEL
2.Go to Formula bar.
3.In formula bar enter the function as“=TINV”
4.Enter the probability as 0.05.
5.Enter the degrees of freedom as 23.
6.Click enter
EXCEL output:
From the EXCEL output, the critical value of t at the 0.95 confidence level with the 23 degrees of freedom is 2.069.
Thus, the critical value of t is 2.069.
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