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

Answer:

She needs a sample size of 25.

Step-by-step explanation:

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

$\alpha = \frac{1 - 0.68}{2} = 0.16$

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

$M = z\frac{\sigma}{\sqrt{n}}$

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

$M = z\frac{\sigma}{\sqrt{n}}$

$0.4 = 0.995\frac{2}{\sqrt{n}}$

$\sqrt{n} = \frac{0.995*2}{0.4}$

$(\sqrt{n})^2 = (\frac{0.995*2}{0.4})^2$

$n = 24.8$

Rounding up:

She needs a sample size of 25.