Question

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 population SD is 2 grams. What is the minimum sample size she needs to create a confidence interval that has a width of 0.4 grams?

Answer 1

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.