Statistics VCAA sample paper question

[dooyeon1998]

Hello guys. I'm basing this question off the VCAA 2016 specialist maths sample exam 2 question 6 extended response

A part of the question states "When checked, a random sample of n = 25 such computers is
found to have an average lifetime of x = 9.7 hours and a standard deviation of s = 1 hour."

and then later says that "Assume that the distribution of lifetimes is normal and that s is a sufficiently accurate estimate of
the population (of lifetimes) standard deviation σ."

How I interpreted this information was that the standard deviation of the sample was 1, not the standard deviation of the population. So I assumed that you could use standard deviation = 1 to find the p value. Not 1/(25)^0.5 =0.2.

I am just confused and appreciate any clarification.

[SJS]

Hey, I came across this in the sample exam as well, and also in the Checkpoints question. I *think* I get it, so heres my explanation since no one else is answering.

Standard deviation of the sample is 1, therefore the standard deviation of the distribution of sample means (AKA standard error) is estimated to be 1/(25)^0.5 = 0.2.

This comes from SD_of_sample_means=s/(n)^0.5. You're trying to find the SD of the distribution of sample means, not the SD of the sample. From the central limit theorem, it is the distribution of sample means which is approximated to a normal distribution. It is with this distribution that we decide whether of not our sample mean is close enough to the expected sample mean (i.e. the alleged population mean) to accept or reject the null hypothesis.

Sam 

[dooyeon1998]

Oh okay cheers I think that made it clear thank you so much !!