Fractions and Decimals

Discrete Mathematics

Differential Equations

Solved on Oct 27, 2023

Find the degrees of freedom for the given t-interval: $\bar{x}=17.598$ , $s_x=16.01712719$ , $n=50$ .

STEP 1

Assumptions1. The sample size is50 (n=50) . The sample mean is17.598 ( $\bar{x}=17.598$ )
3. The sample standard deviation is16.01712719 ( $x=16.01712719$ )
4. The confidence interval is (13.046,22.15)

STEP 2

The number of degrees of freedom for a t-distribution is calculated as the sample size minus1. $df = n -1$

STEP 3

Now, plug in the given value for the sample size to calculate the degrees of freedom.
$df =50 -1$

STEP 4

Calculate the degrees of freedom.
$df =50 -1 =49$ The number of degrees of freedom that should be used for finding the critical value $t_{\alpha /2}$ is49.

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