For an alpha level of 0.05, the critical value of t0 would be 2.262. For an alpha level of 0.01, the critical value of t0 would be 3.250 with an unknown variance.
Significance Level (alpha) | Critical Value (t0)
-------------------------------------------
0.10 | 1.833
0.05 | 2.262
0.01 | 3.250
To test the hypothesis that the population mean is equal to 10 against the alternative that the population mean is greater than 10 with an unknown variance, we would use a one-tailed t-test. The critical value of a t-test is determined by the alpha level, which is the probability of rejecting the null hypothesis given that it is true. The lower the alpha level, the higher the critical value of t0. For an alpha level of 0.10, the critical value of t0 would be 1.833. For an alpha level of 0.05, the critical value of t0 would be 2.262. For an alpha level of 0.01, the critical value of t0 would be 3.250.
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