Formula for calculating the confidence level of a given confidence interval

Say I have a sample size of 36 with a sample mean of 115 and sample standard deviation of 45. I'm given a confidence interval of between 100 and 130. I'd like to calculate the associated confidence level. I know the general procedure for calculating this, but was wondering if this a general, single, formula for determining the associated confidence level? Assume a normal population distribution.

• Do you know if the population being sampled from is normally distributed? – Silverfish Sep 17 '16 at 18:24
• @Silverfish - Yes, thank you. I updated my post. – Randy Minder Sep 17 '16 at 18:25
• 1. Is this a CI for a mean or something else? 2. What's the general procedure you know? It may be easier for you to follow in context of what you know – Glen_b Sep 18 '16 at 7:40

Assuming your confidence interval is for the mean, you can work backwards from the formula for the confidence interval margin of error: $$MOE=\frac{SD}{\sqrt{n}}*t_{crit}(C,n-1)$$ And knowing from this example that $MOE=115-100$, $SD=45$, and $n=36$, we can fill in the following to solve for $C$: $$15=\frac{45}{\sqrt{36}}*t_{crit}(35,C)$$ $$t_{crit}(35,C)=2$$ Then we can use a critical $t$ table or calculator to see what $C$ level corresponds to 2.00 for 35 degrees of freedom.
Here, $C=95$% or $\alpha=.05$ for two tailed tests