# Finding Sample Standard Deviation Help

• Mar 13th 2014, 07:35 AM
Hiccups
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.
• Mar 13th 2014, 08:17 AM
Shakarri
Re: Finding Sample Standard Deviation Help
The margin of error formula is $E=Z_{1-\alpha /2} \frac{\sigma}{\sqrt{n}}$
• Mar 13th 2014, 08:23 AM
Hiccups
Re: Finding Sample Standard Deviation Help
Quote:

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.
• Mar 13th 2014, 08:31 AM
Shakarri
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 $\sigma$
• Mar 13th 2014, 08:35 AM
Hiccups
Re: Finding Sample Standard Deviation Help
Quote:

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.
• Mar 13th 2014, 08:41 AM
Shakarri
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
• Mar 13th 2014, 08:44 AM
Hiccups
Re: Finding Sample Standard Deviation Help
Quote:

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?
• Mar 13th 2014, 08:55 AM
Shakarri
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
• Mar 13th 2014, 08:57 AM
Hiccups
Re: Finding Sample Standard Deviation Help
Quote:

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..?
Attachment 30404
• Mar 13th 2014, 09:23 AM
Shakarri
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
• Mar 13th 2014, 10:10 AM
Hiccups
Re: Finding Sample Standard Deviation Help
Quote:

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?
• Mar 13th 2014, 11:58 AM
Hiccups
Re: Finding Sample Standard Deviation Help
I keep getting an answer of 20.408 and I know that isn't correct..
• Mar 14th 2014, 03:43 AM
Shakarri
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