Q6.4☆ Points: 2 Suppose that Angela wants to use her sample to create a 68% confidence interval for the true population median of boba weight per drink and she knows that the po…

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asked May 21, 2022 9.5k views

1 Answer

Manik Magar · Answer 1 · 2022-05-26T22:55:51+0000

Answer:

She needs a sample size of 25.

Explanation:

We have that to find our
$\alpha$ level, that is the subtraction of 1 by the confidence interval divided by 2. So:

$\alpha = (1 - 0.68)/(2) = 0.16$

Now, we have to find z in the Ztable as such z has a pvalue of
$1 - \alpha$ .

That is z with a pvalue of
1 - 0.16 = 0.84 , so Z = 0.995.

Now, find the margin of error M as such

$M = z(\sigma)/(√(n))$

In which
$\sigma$ is the standard deviation of the population and n is the size of the sample.

The population SD is 2 grams.

This means that
$\sigma = 2$

What is the minimum sample size she needs to create a confidence interval that has a width of 0.4 grams?

She needs a sample size of n.

n is found when M = 0.4. So

$M = z(\sigma)/(√(n))$

0.4 = 0.995(2)/(√(n))

√(n) = (0.995*2)/(0.4)

(√(n))^2 = ((0.995*2)/(0.4))^2

n = 24.8

Rounding up:

She needs a sample size of 25.