Question

determine the t - value in each of the cases
click the icon to view the table of areas under the t - distribution.
(a) find the t - value such that the area in the right tail is 0.25 with 5 degrees of freedom
0.727 (round to three decimal places as needed)
(b) find the t - value such that the area in the right tail is 0.15 with 13 degrees of freedom
1.079 (round to three decimal places as needed)
(c) find the t - value such that the area left of the t - value is 0.025 with 19 degrees of freedom hint: use symmetry

• 2.093 (round to three decimal places as needed)

(d) find the critical t - value that corresponds to 90% confidence. assume 29 degrees of freedom
(round to three decimal places as needed.)

Explanation:

Step1: Calculate the significance level

For a \(90\%\) confidence level, the significance level \(\alpha = 1 - 0.90=0.10\).

Step2: Determine the area in one - tail

Since it is a two - tailed test (for confidence intervals), the area in each tail is \(\frac{\alpha}{2}=\frac{0.10}{2} = 0.05\).

Step3: Use the t - distribution table

We have \(n - 1=29\) degrees of freedom. Looking up the value in the t - distribution table with \(\text{df}=29\) and right - tail area \(0.05\).

Answer:

\(1.699\)