How to use a reference table to determin if a sample mean is consistent with population

I have a sample of people (n=36) with a mean cholesterol level of 4.1. The reference table states that the normally distributed population has values between 3.2 and 6.2 (95% confidence interval).

Can I conclude that the sample group has a different cholesterol value than “the normal population”? I have to solve this using a significance level of 0.05, showing all steps required.

I honestly have no idea where to start, but this is how I tried:

xbar = 4.1
n = 36
pop.mean = 4.7 (right?)


I was trying to get the sample standard deviation from the population sd, but I'm not sure if that's possible at all. And that's where I'm stuck. How do I need to approach this?

• Where is the 4.7 population mean coming from? Where is the .76 population standard deviation coming from? Also, if this is homework please add the "self-study" tag. – TrynnaDoStat Feb 4 '15 at 21:51
• Yes, this is a homework task - sorry, I didn't know about the self study tag. I took th emean from the provided confidence interval (95%) (3.2+6.2)/2 to get the population mean, and then tried to calculate the population standard deviation based on the fact that the upper lever equals µ+1.96σ. And please correct me if I already screwed up on this. How would I approach this to conclude that the sample group has a different cholesterol value than the population? – derBrain Feb 4 '15 at 22:10

The assumption of a normal distribution may be heroic here. If the assumption may be made then I assume that your population standard deviation is half the range of the population 95% confidence range divided by 1.96. In that case the standard deviation of an estimate of the mean of a sample of size $n$ is (population s. d.)/$\sqrt{n}$. You can then use this estimate to test if the sample mean is within the 95% range for a samp[le mean drayn from a normal distriution.
• If the population mean is 4.7 then a 95% confidence limit for the mean of size n is (4.7-1.96 * (populatio s.d.)/$\sqrt(n)$ , 4.7+1.96 * (populatio s.d.)/$\sqrt(n)$ ). What is the probability that a sample of 36 with mean 4.1 was drawn from that population – John C Frain Feb 5 '15 at 23:33