Question 2 4 points Save An A consumer agency is investigating claims that the four soda...

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Answer 1

Answer #1

The confidence interval refers to the range of values for which the experimenter is fairly sure that the data points lie in.

The confidence interval is given by the formula:

$CI = \bar{x} \pm z\frac{\sigma}{\sqrt{n}}$

where x_bar is the mean, sigma is the standard deviation and n is the number of data points. z is a number that refers to the %CI required.

For a 90%CI, the value of z = 1.645.

We have to find the 90%CI for Machine 2.

For machine 2, we have

$\bar{x} = 16.09$

$\sigma^2 =0.00212$

$\therefore \sigma =\sqrt{0.00212} = 0.046$

The number of data-points for Machine 2 is n=6.

Substituting these values in the CI formula, we have:

$90\% CI = 16.09 \pm 1.645\times\frac{0.046}{\sqrt{6}}$

$\therefore 90\% CI = 16.09 \pm 1.645\times\frac{0.046}{2.45} = 16.09 \pm 1.645\times0.019$

$\therefore 90\% CI = 16.09 \pm 0.031255$

$\therefore 90\% CI = (16.09 - 0.031255, 16.09 + 0.031255)$

$\therefore 90\% CI = (16.05875, 16.1213)$

The upper bound refers to the largest value that falls under this 90% CI.

This value is 16.1213.

Answer 2