# Thread: Confidence interval-population standard deviation unknown

1. ## Confidence interval-population standard deviation unknown

Help!!!! Homework problem:

The amounts of juice (in ounces) in 8 randomly selected juice bottles are:

15.1, 15.1, 15.6, 15.6, 15.2, 15.4, 15.3, 15.8

Find the confidence interval for the population standard deviation.

2. Originally Posted by Gail
Help!!!! Homework problem:

The amounts of juice (in ounces) in 8 randomly selected juice bottles are:

15.1, 15.1, 15.6, 15.6, 15.2, 15.4, 15.3, 15.8

Find the confidence interval for the population standard deviation.
You will first need your mean and standard deviation ( $\mu$ and $\sigma$ of your juice bottle set.

Copy the number set above and enter it here:

Mean, Variance, and Standard Deviation

I get $\mu = 15.3875$
$\sigma^2 = 0.05859$
$\sigma = 0.2421$

EDIT - I think since you asked for standard deviation, you need to go here instead: Estimating a population standard devation or variance

3. Ok, I read more at the link above, and was able to match their numbers to the decimal point using the program I attached. I've filled in the values for your problem and the answers are attached. Let me know if you have questions.

To prove this, plug in their confidence interval of 99 and their N value of 101 and see how we match the numbers for the National Center for Educational Statistics example.

When I get home from work, I'll try to build a lesson with the math homework line by line this weekend and PM you in case you have other problems like this one in the future.

http://www.mathhelpforum.com/math-he...tml#post124705

Edit, new attachment.

4. ## New Lesson

Ok, as promised, here is a much, much more detailed answer to your question.

Go here --> Chi-Squared Confidence Interval for Estimation of Variance and Standard Deviation

Take a look at the instructions link quickly at the top of the page. Your N is obviously 8, your variance is the one you calculated from my lesson I posted above for mean, standard deviation, and variance. This variance was 0.05859. Your Confidence percentage was not stated, so you can use any confidence percentage from 95 - 99 if you want. This will give you a confidence interval for either standard deviation or variance. In addition, towards the bottom of the math work, there are 2 special notes I put in there for you or anybody else for how to calculate the chi-squared values using Excel.

Using a 99% confidence interval, I get 0.1422 < $\sigma$ < 0.6439 for the standard deviation.

For future reference, this lesson is found on the statistics menu of my page under "Confidence Intervals". The lesson is searchable by the following keywords at my site as well:
Calculates, confidence, interval, standard, deviation, variance, Chi-Squared, method, degrees, freedom.

As always, let me know if you have questions or want enhancements on the lesson. There are a few greek symbols on there, let me know if you cannot see them.