You are told that a 95% CI for expected lead content when traffic flow is 15, based on a sample of n = 12 observations, is (461.2, 598.6). Calculate a CI with confidence level 99% for expected lead content when traffic flow is 15

The margin of error is given by:

For 95% of confidence the value of the significance is and , the degrees of freedom are given by:

And then we can calculate the critical value for 95% with df = 11 and we got

And then we can find the standard error:

And using the confidence interval formula we got:

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

represent the sample mean for the sample  

population mean (variable of interest)

s represent the sample standard deviation

n represent the sample size  

Solution to the problem

The confidence interval for the mean is given by the following formula:

  (1)

For the 95% confidence interval we know that the result is given by (461.2, 598.6), we can estimate the sample mean like this:

Because the distribution is symmetrical, now we can estimate the width of the interval like this:

And the margin of error is given by:

The margin of error is given by:

For 95% of confidence the value of the significance is and , the degrees of freedom are given by:

And then we can calculate the critical value for 95% with df = 11 and we got

And then we can find the standard error:

The standard error is given by

Now we are interested for the 99% confidence interval, so then we need to find a new critical value for this confidence level and we got:

And using the confidence interval formula we got: