Answer:
Interval [16.34 , 21.43]
Step-by-step explanation:
First step. Calculate the mean
[tex]\bar X=\frac{(23+18+23+12+13+23)}{6}=18.666[/tex]
Second step. Calculate the standard deviation
[tex]\sigma =\sqrt{\frac{(23-18.666)^2+(18-18.666)^2+(23-18.666)^2+(12-18.666)^2+(13-18.666)^2+(23-18.666)^2}{6}}[/tex]
[tex]\sigma=\sqrt\frac{18.783+0.443+18.783+44.435+5.666+18.783}{6}[/tex]
[tex]\sigma=\sqrt{17.815}=4.22[/tex]
As the number of data is less than 30, we must use the t-table to find the interval of confidence.
We have 6 observations, our level of confidence DF is then 6-1=5 and we want our area A to be 80% (0.08).
We must then choose t = 1.476 (see attachment)
Now, we use the formula that gives us the end points of the required interval
[tex]\bar X \pm t\frac{\sigma}{\sqrt n}[/tex]
where n is the number of observations.
The extremes of the interval are then, rounded to the nearest hundreth, 16.34 and 21.43
