Final answer:
The critical t value for a two-sided 95% confidence interval with 19 degrees of freedom is 2.093, which is used to calculate the confidence interval around a sample mean or other statistics. This t value will change if the degrees of freedom change due to a larger sample size.
Step-by-step explanation:
The critical t value for a two-sided 95% confidence interval when the degrees of freedom (df) are 19 is 2.093. This value is calculated using a t-distribution table or a calculator function like invT. To determine this t value, one would use the invT function with the area to the left of the critical value, which in this case for a two-tailed test would be 0.975 (since we are leaving 2.5% in each tail for a total of 5% probability in the tails with a 95% confidence level). The value of 2.093 is then used to calculate the confidence interval of any given statistic.
For example, if the sample mean is 41, the 95% confidence interval would include this value adjusted by the margin of error, which is computed by multiplying the t value by the standard error. If the sample size is increased, say to 30 or 50, the degrees of freedom will also increase, and the t value will slightly decrease (meaning that the interval will be narrower), as seen in the t-distribution tables or by calculating with the calculator function.