SOLUTION: Assuming that the population standard deviation is unknown for a randomly selected sample whose size is 11, sketch the rejection region for a one-tailed test with 99% confidence.

Question 1181433: Assuming that the population standard deviation is unknown for a
randomly selected sample whose size is 11, sketch the rejection region
for a one-tailed test with 99% confidence. Does t = 2.86 fall in the
rejection region?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
if you don't know the population standard deviation, then you're looking at a t-score with a sample size of 11 which gives you a t-score with 11 - 1 = 10 degrees of freedom.
with a one-tailed test at 99% confidence level, the critical alpha on the right side of the distribution will be .01.
the critical alpha is used to find the critical t-score.
looking up a one tailed critical alpha of .01 in the critical t-score tables gets you a critical t-score of 2.764 with 10 degrees of freedom.
your test t-score of 2.86 with 10 degrees of freedom would reside in the rejection region because it's greater than the critical t-score.
my sketch looks like this.

any area to the right of the critical t-score is in the rejection zone.

the t-score table i used gives you the critical t-score with 10 degrees of freedom as shown below.

you choose one tailed alpha of .01 and then look for the corresponding t-score with 10 degrees of freedom.

that's your critical t-score based on the critical one teiled alpha.

you can graph the t-score using the t-score graphinc calculator found at https://mathcracker.com/t-distribution-graph-generator#results

the graphs are shwn below.
first graph is t-score of 2.764.
second graph is t-score of 2.86.

since the t-score of 2.86 is greater than the critical t-score of 2.764, you are in the rejection zone.

since you are in the rejection zone, the test t-score of 2.86 give you a smaller area to the right of it as the critical z-score of 2.764.

the critical alpha is .01.
the test alpha is .0085

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