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Find the critical value t_(c) for the confidence level c=0.80 and sample size n=9.
t_(c)=◻ (Round to the nearest thousandth as needed.)

Find the critical value $t_{c}$ for the confidence level $c=0.80$ and sample size $n=9$ . $\newline$ $t_{c}=\square$ (Round to the nearest thousandth as needed.)

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Find values of normal variables

Full solution

Q. Find the critical value

t_{c}

for the confidence level

c=0.80

and sample size

n=9

.

\newline

t_{c}=\square

(Round to the nearest thousandth as needed.)

Calculate Degrees of Freedom: Determine the degrees of freedom for the t-distribution. The degrees of freedom (df) for a sample size $n$ is given by $df = n - 1$ . For a sample size of $n = 9$ , the degrees of freedom is $df = 9 - 1 = 8$ .
Identify Upper Tail Area: Identify the area in the upper tail for the given confidence level. $\newline$ The confidence level is $c = 0.80$ , which means the area in both tails combined is $1 - c = 0.20$ . Since the t-distribution is symmetric, the area in each tail is $0.20 / 2 = 0.10$ .
Find Critical t-Value: Use the t-distribution table to find the critical t-value. For $df = 8$ and an area of $0.10$ in the upper tail, we look up the t-distribution table to find the corresponding t-value. According to the table, the critical t-value for $df = 8$ and an upper tail area of $0.10$ is approximately $1.397$ .
Round to Nearest Thousandth: Round the critical $t$ -value to the nearest thousandth. $\newline$ The critical $t$ -value from the table is $1.397$ , which is already rounded to the nearest thousandth.

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