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.

  • $\begingroup$ Do you know if the population being sampled from is normally distributed? $\endgroup$ – Silverfish Sep 17 '16 at 18:24
  • $\begingroup$ @Silverfish - Yes, thank you. I updated my post. $\endgroup$ – Randy Minder Sep 17 '16 at 18:25
  • $\begingroup$ 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 $\endgroup$ – 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


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.