Final answer:
The lower tail area with 50 degrees of freedom for a two-sided 95% confidence interval is 0.025.
Step-by-step explanation:
The lower tail area with 50 degrees of freedom refers to the cumulative probability from the left end of the distribution up to a point. When constructing a two-sided 95 percent confidence interval, the probability excluded from the interval is split evenly between the upper and lower tails of the distribution, which amounts to 5 percent in total or 2.5 percent in each tail (0.025). Therefore, the lower tail area with 50 degrees of freedom, for a two-sided 95 percent confidence level, is 0.025.
It looks like you are referring to the critical values or percentiles of the t-distribution with 50 degrees of freedom and a two-tailed test. The lower tail area refers to the probability that a random variable from a t-distribution with 50 degrees of freedom is less than a certain value.
For a two-tailed test with a significance level of, say, 0.05, the lower tail area would be half of that (0.025). If you're looking for a specific significance level, you may use the following values:
0.05 corresponds to a two-tailed test with a significance level of 0.10.
0.025 corresponds to a two-tailed test with a significance level of 0.05.
0.01 corresponds to a two-tailed test with a significance level of 0.02.
0.005 corresponds to a two-tailed test with a significance level of 0.01.