Question

a t distribution with 6 degrees of freedom is graphed below. the region under the curve to the right of t 0.96 is shaded. the area of this region is 0.96.
find the value of t 0.96. round your answer to three decimal places.
t 0.96 = □

Explanation:

Step1: Recall the t - distribution property

For a t - distribution with \(n\) degrees of freedom, we can use the t - table or statistical software. Here \(n = 6\).

Step2: Use the t - distribution table or software

Using a t - distribution table (or a calculator with t - distribution functionality, e.g., in R: qt(1 - 0.96, 6)), we look for the value of \(t\) such that the area to the right of \(t\) is \(0.96\).

In R, when we run the code qt(1 - 0.96, 6), the formula for the quantile function of the t - distribution \(t_{\alpha,n}\) where \(\alpha\) is the significance level and \(n\) is the degrees of freedom. Here \(\alpha=0.96\), and \(n = 6\).

The calculation gives us \(t=- 1.943\) (since the t - distribution is symmetric, and if the area to the right is large (\(>0.5\)), the \(t\) - value is negative).

Answer:

\(-1.943\)