3 years ago

Which symbol replaces ? To make the statement true?

Mathematics

1 answer:

DedPeter [7]3 years ago

8 0

A is the correct answer.

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1,100

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OlgaM077 [116]

Answer:

Interval [16.34 , 21.43]

Step-by-step explanation:

First step. <u>Calculate the mean</u>

$\bar X=\frac{(23+18+23+12+13+23)}{6}=18.666$

Second step. <u>Calculate the standard deviation</u>

$\sigma =\sqrt{\frac{(23-18.666)^2+(18-18.666)^2+(23-18.666)^2+(12-18.666)^2+(13-18.666)^2+(23-18.666)^2}{6}}$

$\sigma=\sqrt\frac{18.783+0.443+18.783+44.435+5.666+18.783}{6}$

$\sigma=\sqrt{17.815}=4.22$

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

$\bar X \pm t\frac{\sigma}{\sqrt n}$

where n is the number of observations.

The extremes of the interval are then, rounded to the nearest hundreth, 16.34 and 21.43

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3 years ago