Question 1163032: We use the t distribution to construct a confidence interval for the population mean when the underlying population standard deviation is not known. Under the assumption that the population is normally distributed, find tα/2,df for the following scenarios. (You may find it useful to reference the t table. Round your answers to 3 decimal places.)
tα/2,df
a. A 95% confidence level and a sample of 18 observations.
b. A 99% confidence level and a sample of 18 observations.
c. A 95% confidence level and a sample of 9 observations.
d. A 99% confidence level and a sample of 9 observations.
Please label answers by a., b., c., and d.
Thank you very much! I appreciate it!
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website!
Your teacher is asking you to find t critical values based on the significance level (alpha) and the sample size (n).
For each of these problems, I'm going to use this T table
http://www.ttable.org/
which a similar table is likely in the back of your statistics textbook
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Part A
We have a sample size of n = 18. The degrees of freedom (df) is df = n-1 = 18-1 = 17. We will solely focus on the df = 17 row of the table. I recommend highlighting it or circling the row with a different color.
The confidence level is 95%, which leaves 1-0.95 = 0.05 as the area in both tails combined. Look at the top of the table where it says "two-tails". Along this row, locate 0.05 and highlight the entire column. This is what we have after highlighting the proper row and column mentioned.
The value 2.110 is in this row and column combo. Therefore, the critical t value is 2.110 when we have 95% confidence and df = 17.
This means  \approx 0.95) when df = 17.
Answer: 2.110
You could use the tCDF function on your TI calculator to get the same approximate result. Of course your calculator is going to give a more accurate answer (there's only so much room on a table and we have to be able to fit a lot of values; so rounding is inevitable).
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Part B
Same idea as part A. We have df = 17 since n hasn't changed. The confidence level is different though. We have 1-0.99 = 0.01 as the total area in both tails combined. Look at 0.01 in the "two tails" row and highlight the entire column.
Answer: 2.898
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Part C
Now we have df = n-1 = 9-1 = 8. We'll use the column that has twotails = 0.05, like we did with part A.
Answer: 2.306
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Part D
We have df = 8 and twotails = 0.01 (see part B). Use the table to find the t critical value.
Answer: 3.355
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