We can find critical value by using t - table. For using t - table we need degree of freedom and alpha either for two tailed test or one tailed test. We can determine degree of freedom by subtracting sample size from one. So in given question sample size is 23. So we can say degree of freedom(df) for sample size 23 is df = 23 - 1= 22 Now we have to go on row for degree of freedom 22.
After that we need to find alpha either for two tailed test or one tailedl test. Confidence level is 99%. We can convert it into decimal as 0.99.
So alpha for two tailed test is 100 - 0.99 = 0.01
Alpha for one tailed test is 0.01/2 = 0.005.
So we will go on column for 0.01 for two tailed test alpha or 0.005 for one tailed test alpha. SO the critical value 22 degree of freedom and 0.01 two tailed alpha is 2.819 from t - table.
