T Distribution Explanation 486F09
1. The user asks to explain well with the tPx, which likely refers to the t-distribution probability expression $t_{p,x}$ or a similar statistical notation.
2. Let's clarify the problem: Suppose we want to find the t-value corresponding to a given probability $p$ and degrees of freedom $x$ in a t-distribution.
3. The t-distribution is used in statistics when estimating the mean of a normally distributed population in situations where the sample size is small and population standard deviation is unknown.
4. The formula or concept used is the inverse cumulative distribution function (CDF) of the t-distribution, often denoted as $t_{p,x}$, which gives the t-score such that the area under the t-distribution curve to the left of $t_{p,x}$ is $p$.
5. To find $t_{p,x}$, you use statistical tables or software functions that compute the inverse t-distribution.
6. For example, if $p=0.95$ and degrees of freedom $x=10$, $t_{0.95,10}$ is the t-value where 95% of the distribution lies to the left.
7. This value is important in hypothesis testing and confidence interval calculations.
8. In summary, $t_{p,x}$ represents the critical t-value for probability $p$ and degrees of freedom $x$, used to make statistical inferences.