# Math Help - Finding Sample Standard Deviation Help

1. ## Finding Sample Standard Deviation Help

Assume that I created a 95% confidence interval for the mean hours studied for a test based on a sample of 100 students. The lower bound of this interval was 6 and the upper bound was 10. Assume that when I created this interval I knew the population standard deviation.

Calculate and report the population standard deviation.

I knew I use the E = zα/2 * (2√ n) formula (margin of error) but I know how to apply it to this problem. I also found that the sample mean is 8. Im just stuck on how to find the population standard deviation.

2. ## Re: Finding Sample Standard Deviation Help

The margin of error formula is $E=Z_{1-\alpha /2} \frac{\sigma}{\sqrt{n}}$

3. ## Re: Finding Sample Standard Deviation Help

Originally Posted by Shakarri
The margin of error formula is $E=Z_{1-\alpha /2} \frac{\sigma}{\sqrt{n}}$
Yes, I know this but I don't know how to find the population standard deviation from the formula.

4. ## Re: Finding Sample Standard Deviation Help

Ok, you misstyped it in your first post.
Try using the formula for the upper bound of the confidence interval to get $\sigma$

5. ## Re: Finding Sample Standard Deviation Help

Originally Posted by Shakarri
Ok, you misstyped it in your first post.
Try using the formula for the upper bound of the confidence interval to get $\sigma$
Oh, whoops! Haha. I tried but I get stuck on how to figure out the Z portion.

6. ## Re: Finding Sample Standard Deviation Help

For a 95% confidence interval 47.5% of the population is below the mean and 47.5% is above the mean.
You can use this chart to figure out the Z value for the 95% interval Standard Normal Distribution Table

7. ## Re: Finding Sample Standard Deviation Help

Originally Posted by Shakarri
For a 95% confidence interval 47.5% of the population is below the mean and 47.5% is above the mean.
You can use this chart to figure out the Z value for the 95% interval Standard Normal Distribution Table
So would the z value be 1.645?

8. ## Re: Finding Sample Standard Deviation Help

No, you were looking at the situation where 50% is below the mean and 45% is above the mean. When you have 47.5% above the mean Z is equal to 1.96

9. ## Re: Finding Sample Standard Deviation Help

Originally Posted by Shakarri
No, you were looking at the situation where 50% is below the mean and 45% is above the mean. When you have 47.5% above the mean Z is equal to 1.96
Oh! I see, that why I kept getting the wrong answer. So then I would just plug this number into the 'Z' portion of the equation then?
So it would look like this:

4= 1.96 (α/10) ?

Edit: My book is saying that the margin of error equation doesn't include the Z1-α/2 but only the Zα/2 part without 1-. Is that correct..?

10. ## Re: Finding Sample Standard Deviation Help

The margin of error E is the difference between the sample mean and the upper limit, or the sample mean and the lower limit.

For a 95% confidence interval the significance level $\alpha$ is 0.05 (the amount of the population not in the confidence interval)
$\alpha /2=0.025$. $Z_{0.025}$ is the point in the normal distribution that has 2.5% of the population below it, that point is -1.96

$1- \alpha /2=0.975$. $Z_{0.975}$ is the point with 97.5% of the population below it, that point is 1.96.

So it doesn't really matter, all that changes is the sign

11. ## Re: Finding Sample Standard Deviation Help

Originally Posted by Shakarri
The margin of error E is the difference between the sample mean and the upper limit, or the sample mean and the lower limit.

For a 95% confidence interval the significance level $\alpha$ is 0.05 (the amount of the population not in the confidence interval)
$\alpha /2=0.025$. $Z_{0.025}$ is the point in the normal distribution that has 2.5% of the population below it, that point is -1.96

$1- \alpha /2=0.975$. $Z_{0.975}$ is the point with 97.5% of the population below it, that point is 1.96.

So it doesn't really matter, all that changes is the sign
So then would the formula I posted in my previous post be correct to solve for the population standard deviation?

12. ## Re: Finding Sample Standard Deviation Help

I keep getting an answer of 20.408 and I know that isn't correct..

13. ## Re: Finding Sample Standard Deviation Help

E is the difference between the sample mean and the upper limit, you were using the difference between the lower limit and the upper limit