Final answer:
To find the critical value for a sample size of 19 and a 99% confidence level, one would typically use a chi-square table or a t-distribution table for 18 degrees of freedom. A standard normal distribution or F-distribution table would not be appropriate for this context.
Step-by-step explanation:
To find the critical value corresponding to a sample size of 19 and a 99% confidence level, we will use different statistical tables depending on the context. Since the degrees of freedom (df) for the sample size of 19 are 18 (df = n - 1), the critical values can be found as follows:
- Chi-square distribution: Look up the chi-square value in a chi-square table for 18 degrees of freedom at the 99% level.
- Standard normal distribution: The standard normal table is used for a z-distribution, which is not appropriate in this context as we are dealing with a small sample size.
- t-distribution: Consult a t-distribution table using 18 degrees of freedom to find the critical t-value for a 99% confidence level.
- F-distribution: The F-distribution table is used when comparing two variances, which is not the context of this question.
Looking at reference information, we find that a t-value can be obtained from a table or a calculator. For a t-distribution with 18 degrees of freedom and a 99% confidence level, the critical t-value will be higher than for a 95% confidence level, which was 2.093 for 19 degrees of freedom. It is important to note that a t-distribution is used when the population standard deviation is unknown, which seems to be the case here.