Final answer:
The critical value for a two-tailed test with a significance level of 0.01, a sample size of 10, and a null hypothesis of population mean = 8.00 is approximately ±2.821.
Step-by-step explanation:
The critical value for a hypothesis test depends on the significance level (alpha), the sample size, and the degrees of freedom.
In this case, the significance level is 0.01 (or 1% confidence level), the sample size is 10, and the null hypothesis is that the population mean is 8.00.
To find the critical value, we need to determine the degrees of freedom, which is n - 1. In this case, the degrees of freedom is 10 - 1 = 9.
Using the given information, we can refer to a critical value table to find the value for alpha/2 = 0.005 and degrees of freedom = 9.
From the table, the critical value for a two-tailed test is approximately ±2.821.