Question 1166845: For a confidence level of 99% with a sample size of 28, find the critical t value.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! if the sample size is 28, then the degrees of freedom is 1 less than that, making it equal to 27.
you can have a two tail confidence interval or a one tail confidence interval.
you would choose one or the other, depending on whether your t-test is a one-tail test or a two-tail test.
i'm thinking that you are probably looking for the two tail confidence interval, so go with that unless otherwise specified.
however, i'll show you both so you can see how it's done for each.
either way, your degrees of freedom = 27 because your sample size = 28.
here's a picture of the t-score table i found at https://www.sjsu.edu/faculty/gerstman/StatPrimer/t-table.pdf
i showed the top header rows and the 27 degrees of freedom row only.
you can click the link to see the whole table.
for a two-tailed confidence interval at 99% confidence level, each tail will be .5% of the area under the normal distribution curve.
at 27 degrees of freedom, the two tail critical t-score is plus or minus 2.771
for a one-tailed confidence interval of 99%, the single tail will be 1% of the area under the normal distribution curve.
it will either be on the left side of the confidence interval or the right side of the confidence interval.
at 27 degrees of freedom, the one tail critical t-score is plus or minus 2.473.
if the tail is on the left, the critical t-score is -2.473.
if the tail is on the right, the critical t-score is +2.473.
here's a graphic display of what a one tail confidence interval looks like and what a two tail confidence interval looks like.
it is not drawn to scale, but should be good enough for you to get a general idea of what is meant.
the two tail confidence interval has tails on both sides.
the one tail confidence interval has one tail either on the left or on the right.
note that the rate is shown instead of the percent.
1% = .01
.5% = .005
99% = .99
rate = rate percent divided by 100
rate percent = rate * 100
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