# Statistical analysis

• Oct 21st 2012, 04:21 PM
fara
Statistical analysis
1. It is known that normal human body temperature is 98.4oF. A nurse measured the body temperature of 36 sore throat children and obtained their mean body temperature was 98.9oF and standard deviation was 0.5oF. Is sore throat is the reason for the cause the fever to the children?
• Oct 21st 2012, 06:34 PM
chiro
Re: Statistical analysis
Hey fara.

The first thing in these kinds of problems is to come up with a statement (statistical that is) that differentiates between a positive result that contributes to one decision and another that contributes to its complement.

In your question you are trying to see whether the sore throat is the reason, but how do you evaluate this? You can't really make a conclusion of this even with the limited information you have.

But what you can do is provide evidence that people with sore throats have abnormal temperature in that the abnormal temperature is statistically significantly different from the normal temperature and this is given by a 1-sample t-test where you are comparing whether the population mean of a sample is statistically significantly similar or different from a particular value.

The value you are testing is the normal temperature which is 98.4F where the sample mean 98.9F with a standard error of 0.5F. Your test will be that H0: mu = 98.4 and H1: mu != 98.4.

Before we continue what do you know about 1-sample t-tests?
• Oct 21st 2012, 07:49 PM
fara
Re: Statistical analysis
I tried to solve the question according to what you've said; by comparing whether it is similar or significantly different. and from my understanding it is supposed to be two tailed test instead of one tailed test since it doesnt involve comparison of which one is greater or less, and since the sample is more than 30, so i use z test. am i right up until now?
• Oct 21st 2012, 08:57 PM
MaxJasper
Re: Statistical analysis
$P\left(\left.\mu >\mu _0\right|\sigma ,\nu \right)=0.16209$ >0.05 so you can accept (p>0.05) the null hypothesis that 36 kids with sore throats have no fever (Lipssealed)
• Oct 21st 2012, 08:57 PM
chiro
Re: Statistical analysis
You can use the Z-test for large enough sample and you have the right idea.

Just for future reference, remember that if you are dealing with a sample error that is calculated from your sample rather than knowing the population standard deviation or variance, you use a t-test and in the case of a large sample size, as you have pointed out this becomes close enough to normal so that a normal approximation is used.
• Oct 21st 2012, 11:39 PM
fara
Re: Statistical analysis
Quote:

Originally Posted by MaxJasper
$P\left(\left.\mu >\mu _0\right|\sigma ,\nu \right)=0.16209$ >0.05 so you can accept (p>0.05) the null hypothesis that 36 kids with sore throats have no fever (Lipssealed)

how did you get 0.16209?
• Oct 21st 2012, 11:46 PM
fara
Re: Statistical analysis
Quote:

Originally Posted by chiro
You can use the Z-test for large enough sample and you have the right idea.

Just for future reference, remember that if you are dealing with a sample error that is calculated from your sample rather than knowing the population standard deviation or variance, you use a t-test and in the case of a large sample size, as you have pointed out this becomes close enough to normal so that a normal approximation is used.

I misunderstood your first question about 1 sample t-test as 'one tailed test by using t table' when they are completely two different things! My lecturer never mentioned about 1 sample t-test during the lecture before. So i'm a bit lost now. my friend used OTT with Ho : miu = 98.9 Ha : miu < 98.9 ; which is different answer from mine. help please? ^^;